Proceedings of the American Mathematical Society最新文献

英文中文

Lie semisimple algebras of derivations and varieties of PI-algebras with almost polynomial growth 具有几乎多项式增长的导数的列半简单代数和 PI 代数品种

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-05-01 DOI: 10.1090/proc/16896

Sebastiano Argenti

We consider associative algebras with an action by derivations by some finite dimensional and semisimple Lie algebra. We prove that if a differential variety has almost polynomial growth, then it is generated by one of the algebras U T 2 ( W λ ) UT_2(W_lambda ) or E n d ( W μ ) End(W_mu ) for some integral dominant weight λ , μ lambda ,mu with μ ≠ 0 mu neq 0 . In the special case L = s l 2 L=mathfrak {sl}_2 we prove that this is a sufficient condition too.

我们考虑的是具有某种有限维半简单李代数派生作用的关联代数。我们证明，如果一个微分方程具有几乎多项式的增长，那么它是由 U T 2 ( W λ ) UT_2(W_lambda)或 E n d ( W μ ) End(W_mu ) 中的一个代数生成的，对于某个积分主重 λ , μ lambda ,mu μ ≠ 0 mu neq 0。在 L = s l 2 L=mathfrak {sl}_2 的特殊情况下，我们证明这也是一个充分条件。

{"title":"Lie semisimple algebras of derivations and varieties of PI-algebras with almost polynomial growth","authors":"Sebastiano Argenti","doi":"10.1090/proc/16896","DOIUrl":"https://doi.org/10.1090/proc/16896","url":null,"abstract":"We consider associative algebras with an action by derivations by some finite dimensional and semisimple Lie algebra. We prove that if a differential variety has almost polynomial growth, then it is generated by one of the algebras <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper U upper T 2 left-parenthesis upper W Subscript lamda Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">UT_2(W_lambda )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> or <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E n d left-parenthesis upper W Subscript mu Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">End(W_mu )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for some integral dominant weight <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda comma mu\"> <mml:semantics> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">lambda ,mu</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu not-equals 0\"> <mml:semantics> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mu neq 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In the special case <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L equals German s German l Subscript 2\"> <mml:semantics> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"fraktur\">s</mml:mi> <mml:mi mathvariant=\"fraktur\">l</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">L=mathfrak {sl}_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> we prove that this is a sufficient condition too.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"214 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Some maximum principles for parabolic mixed local/nonlocal operators 抛物线局部/非局部混合算子的一些最大原则

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-05-01 DOI: 10.1090/proc/16899

Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci

The goal of this paper is to establish new Maximum Principles for parabolic equations in the framework of mixed local/nonlocal operators.

In particular, these results apply to the case of mixed local/nonlocal Neumann boundary conditions, as introduced by Dipierro, Proietti Lippi, and Valdinoci [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp. 1093–1166].

Moreover, they play an important role in the analysis of population dynamics involving the so-called Allee effect, which is performed by Dipierro, Proietti Lippi, and Valdinoci [J. Math. Biol. 89 (2024), Paper No. 19]. This is particularly relevant when studying biological populations, since the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction.

本文的目的是在混合局部/非局部算子的框架内建立抛物方程的新最大原则。特别是，这些结果适用于混合局部/非局部诺伊曼边界条件的情况，正如迪皮埃罗、普罗埃蒂-利皮和瓦尔迪诺奇所介绍的那样[Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp.］此外，它们在涉及所谓阿利效应的种群动态分析中也发挥着重要作用，迪皮埃罗、普罗埃蒂-利皮和瓦尔迪诺奇[J. Math. Biol. 89 (2024)，论文编号 19]对此进行了研究。在研究生物种群时，这一点尤为重要，因为阿利效应可以检测到一个临界密度，低于这个密度，种群就会严重濒危，面临灭绝的危险。

引用次数: 0

SAT actions of discrete quantum groups and minimal injective extensions of their von Neumann algebras 离散量子群的 SAT 作用及其冯诺伊曼代数的最小注入扩展

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-24 DOI: 10.1090/proc/16882

Mehrdad Kalantar, Fatemeh Khosravi, Mohammad Moakhar

We introduce a natural generalization of the notion of strongly approximately transitive (SAT) states for actions of locally compact quantum groups. In the case of discrete quantum groups of Kac type, we show that the existence of unique stationary SAT states entails rigidity results concerning injective extensions of quantum group von Neumann algebras.

我们为局部紧凑量子群的作用引入了强近似传递（SAT）态概念的自然概括。在 Kac 型离散量子群的情况下，我们证明了唯一静止 SAT 状态的存在会带来关于量子群冯-诺伊曼代数注入扩展的刚性结果。

引用次数: 0

A note on almalgamated free products 关于无汞齐化产品的说明

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16791

Qihui Li, Don Hadwin, Junhao Shen

We prove a general result concerning properties preserved under certain amalgamated free products.

我们证明了一个关于在某些汞齐化自由乘积下保留的性质的一般结果。

引用次数: 0

Hyperfiniteness for group actions on trees 树上群作用的超有限性

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16851

Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko, Pieter Spaas

We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfiniteness of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite.

我们确定了作用于可数树的可数群的自然条件，这些条件意味着格罗莫夫边界上的诱导作用的轨道等价关系是伯尔超无限的。这个条件的例子包括acylindrical作用。我们还确定了上述条件的自然弱化，这意味着边界作用的度量超有限性。然后，我们将举例说明边界作用不是超有限的树上的群作用。

引用次数: 0

Radon–Nikodým property and Lau’s conjecture 拉顿-尼科戴姆性质和刘氏猜想

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16884

Andrzej Wiśnicki

There is a long-standing problem, posed by A.T.-M. Lau [Fixed point theory and its applications, Academic Press, New York-London, 1976, pp. 121–129], whether left amenability is sufficient to ensure the existence of a common fixed point for every jointly weak ∗ ^{ast } continuous nonexpansive semigroup action on a nonempty weak ∗ ^{ast } compact convex set in a dual Banach space. In this note we discuss the current status of this problem and give a partial solution in the case of weak ∗ ^{ast } compact convex sets with the Radon–Nikodým property.

A.T.-M. Lau [Fixed point theory and its applications, Academic Press, New York-London, 1976, pp.Lau [Fixed point theory and its applications, Academic Press, New York-London, 1976, pp.在本论文中，我们讨论了这一问题的现状，并给出了具有 Radon-Nikodým 性质的弱∗ ^{ast } 紧凑凸集的部分解决方案。

{"title":"Radon–Nikodým property and Lau’s conjecture","authors":"Andrzej Wiśnicki","doi":"10.1090/proc/16884","DOIUrl":"https://doi.org/10.1090/proc/16884","url":null,"abstract":"There is a long-standing problem, posed by A.T.-M. Lau [<italic>Fixed point theory and its applications</italic>, Academic Press, New York-London, 1976, pp. 121–129], whether left amenability is sufficient to ensure the existence of a common fixed point for every jointly weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> continuous nonexpansive semigroup action on a nonempty weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact convex set in a dual Banach space. In this note we discuss the current status of this problem and give a partial solution in the case of weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact convex sets with the Radon–Nikodým property.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"68 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strichartz type estimates for solutions to the Schrödinger equation 薛定谔方程解的斯特里查兹类型估计

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16887

Jie Chen

In this article, we show the necessary and sufficient conditions for the inequality <disp-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar u double-vertical-bar Subscript upper L Sub Subscript t Sub Superscript q Subscript upper L Sub Subscript x Sub Superscript r Subscript Baseline less-than-or-equivalent-to double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Subscript Baseline comma"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mrow> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>t</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>x</mml:mi> <mml:mi>r</mml:mi> </mml:msubsup> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">begin{equation*} |u|_{L_t^qL_x^r}lesssim |u|_{X^{s,b}}, end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Baseline colon-equal double-vertical-bar ModifyingAbove u With caret left-parenthesis tau comma xi right-parenthesis mathematical left-angle xi mathematical right-angle Superscript s Baseline mathematical left-angle tau plus StartAbsoluteValue xi EndAbsoluteValue squared mathematical right-angle Superscript b Baseline double-vertical-bar Subscript upper L Sub Subscript tau comma xi Sub Superscript 2"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>≔</mml:mo> <mml:mo fence="false" stretchy="false">‖</mml:mo> <mml:mrow> <mml:mover> <mml:mi>u</mml:mi> <mml:mo stretchy="false">^</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ξ</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mo fence="false" stretchy="false">⟩</mml:mo> <mml:mi>s</mml:mi> </mml:msup> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>+</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <m

在本文中，我们展示了不等式 ‖ u ‖ L t q L x r ≲ ‖ u ‖ X s , b 的必要条件和充分条件。|u|_{L_t^qL_x^r}lesssim |u|_{X^{s,b}}, end{equation*} 其中 ‖ u ‖ X s , b ≔ ‖ u ^ ( τ , ξ ) ξ ⟨ s τ + | ξ | 2 ⟩ b ‖ L τ 、ξ 2 ||u_{X^{s,b}}≔||hat{u}(tau ,xi)（矩形 xi ）（矩形 tau + |xi |^2rangle ^b |{L_{tau,xi}^2}。这些估计也被称为与薛定谔方程有关的斯特里查兹估计。我们还给出了薛定谔方程和艾里方程解的最大函数估计的新证明。

{"title":"Strichartz type estimates for solutions to the Schrödinger equation","authors":"Jie Chen","doi":"10.1090/proc/16887","DOIUrl":"https://doi.org/10.1090/proc/16887","url":null,"abstract":"In this article, we show the necessary and sufficient conditions for the inequality <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u double-vertical-bar Subscript upper L Sub Subscript t Sub Superscript q Subscript upper L Sub Subscript x Sub Superscript r Subscript Baseline less-than-or-equivalent-to double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Subscript Baseline comma\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>t</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>x</mml:mi> <mml:mi>r</mml:mi> </mml:msubsup> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">begin{equation*} |u|_{L_t^qL_x^r}lesssim |u|_{X^{s,b}}, end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Baseline colon-equal double-vertical-bar ModifyingAbove u With caret left-parenthesis tau comma xi right-parenthesis mathematical left-angle xi mathematical right-angle Superscript s Baseline mathematical left-angle tau plus StartAbsoluteValue xi EndAbsoluteValue squared mathematical right-angle Superscript b Baseline double-vertical-bar Subscript upper L Sub Subscript tau comma xi Sub Superscript 2\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mi>u</mml:mi> <mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>≔</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mrow> <mml:mover> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">^</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ξ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> <mml:mi>s</mml:mi> </mml:msup> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>+</mml:mo> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <m","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"47 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nikishin’s theorem and factorization through Marcinkiewicz spaces 尼基申定理和通过马辛凯维奇空间的因式分解

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16888

Mieczysław Mastyło, Enrique Sánchez Pérez

Consider L 0 L^0 , the F F -space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to L 0 L^0 , we prove a theorem that characterizes those maps from any quasi-metric space into L 0 L^0 that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.

L 0 L^0 是有限度量空间上可测函数的所有等价类的 F F 空间，具有度量收敛拓扑。受尼基申关于从巴纳赫空间到 L 0 L^0 的亚线性连续算子因子化的经典结果的启发，我们证明了一个定理，它描述了从任何准度量空间到 L 0 L^0 的映射的特征，这些映射通过 Marcinkiewicz 加权空间强因子化。我们展示了对某类由奥利奇序列空间生成的广义拉德马赫型准巴纳赫空间上的亚线性算子的应用。

{"title":"Nikishin’s theorem and factorization through Marcinkiewicz spaces","authors":"Mieczysław Mastyło, Enrique Sánchez Pérez","doi":"10.1090/proc/16888","DOIUrl":"https://doi.org/10.1090/proc/16888","url":null,"abstract":"Consider <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=\"application/x-tex\">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove a theorem that characterizes those maps from any quasi-metric space into <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A remark on a paper by F. Chiarenza and M. Frasca 对 F. Chiarenza 和 M. Frasca 论文的评论

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16885

N. Krylov

In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of | b u | p |bu|^{p} through the integral of | D u | p |Du|^{p} for p > 1 p>1 . Formally their proof is valid only for d ≥ 3 dgeq 3 . We present here further generalization with a different proof in which D D is replaced with the fractional power of the Laplacian for any dimension d ≥ 2 dgeq 2 .

1990 年，F. Chiarenza 和 M. Frasca 发表论文，将 C. Fefferman 关于 p > 1 p>1 时通过 | D u | p |Du|^{p} 的积分来估计 | b u | p |bu|^{p} 的积分的结果加以推广。形式上，他们的证明仅对 d ≥ 3 dgeq 3 有效。我们在这里用一个不同的证明来进一步概括，在这个证明中，对于任何维度 d ≥ 2 dgeq 2，D D 被替换为拉普拉奇的分数幂。

{"title":"A remark on a paper by F. Chiarenza and M. Frasca","authors":"N. Krylov","doi":"10.1090/proc/16885","DOIUrl":"https://doi.org/10.1090/proc/16885","url":null,"abstract":"In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue b u EndAbsoluteValue Superscript p\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>b</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|bu|^{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> through the integral of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue upper D u EndAbsoluteValue Superscript p\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|Du|^{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p>1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Formally their proof is valid only for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We present here further generalization with a different proof in which <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is replaced with the fractional power of the Laplacian for any dimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 2\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"2 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Pólya’s random walk constants 关于 Pólya 的随机行走常数

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-19 DOI: 10.1090/proc/16854

Robert Gaunt, Saralees Nadarajah, Tibor Pogány

A celebrated result in probability theory is that a simple symmetric random walk on the d d -dimensional lattice Z d mathbb {Z}^d is recurrent for d = 1 , 2 d=1,2 and transient for d ≥ 3 dgeq 3 . In this note, we derive a closed-form expression, in terms of the Lauricella function F C F_C , for the return probability for all d ≥ 3 dgeq 3 . Previously, a closed-form formula had only been available for d = 3 d=3 .

概率论中一个著名的结果是，在 d d 维网格 Z d mathbb {Z}^d 上的简单对称随机行走在 d = 1 , 2 d=1,2 时是经常性的，而在 d ≥ 3 dgeq 3 时是瞬时性的。在本说明中，我们用劳里切拉函数 F C F_C 为所有 d ≥ 3 dgeq 3 的回归概率推导出一个闭式表达式。在此之前，只有 d=3 d=3 时才有闭式公式。

{"title":"On Pólya’s random walk constants","authors":"Robert Gaunt, Saralees Nadarajah, Tibor Pogány","doi":"10.1090/proc/16854","DOIUrl":"https://doi.org/10.1090/proc/16854","url":null,"abstract":"A celebrated result in probability theory is that a simple symmetric random walk on the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\"> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=\"application/x-tex\">d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional lattice <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z Superscript d\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">Z</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {Z}^d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is recurrent for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 1 comma 2\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d=1,2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and transient for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this note, we derive a closed-form expression, in terms of the Lauricella function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript upper C\"> <mml:semantics> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">F_C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, for the return probability for all <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Previously, a closed-form formula had only been available for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d=3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Proceedings of the American Mathematical Society

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀