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On the Commutativity of Closed Symmetric Operators 关于闭对称算子的交换性
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0226-2
S. Dehimi, M. H. Mortad, A. Bachir

In this paper, we mainly show that if a product AB (or BA) of a closed symmetric operator A and a bounded positive operator B is normal, then it is self-adjoint. Equivalently, this means that B commutes with A. Certain generalizations and consequences are also presented.

本文主要证明了如果闭对称算子a和有界正算子B的乘积AB(或BA)是正规的,那么它是自伴随的。等价地,这意味着B与A进行了交换。还给出了一些推广和结果。
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引用次数: 0
On Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators 关于与Schrödinger算子相关的换向子振荡和变分的加权紧性
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0229-z
A. Ge, Q. He, D. Yan

Let ({cal L} = - Delta + V) be a Schrödinger operator with a nonnegative potential V belonging to the reverse Hölder class Bq for q> n/2. In this paper, we study the weighted compactness of oscillation and variation commutators generated by BMO-type functions and some Schrödinger operators, which include Riesz transform and other standard Calderón–Zygmund operators.

设({cal L}=-Delta+V)是一个具有非负势V的Schrödinger算子,其属于q>;n/2.本文研究了由BMO型函数和一些Schrödinger算子(包括Riesz变换和其他标准Calderón–Zygmund算子)生成的振荡和变分换子的加权紧性。
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引用次数: 0
On Meromorphic Solutions of Nonlinear Complex Differential Equations 关于非线性复微分方程的亚纯解
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0225-3
J.-F. Chen, Y.-Y. Feng

By utilizing Nevanlinna theory of meromorphic functions, we characterize meromorphic solutions of the following nonlinear differential equation of the form

$${f^n}{f^prime } + P(z,f,{f^prime }, ldots ,{f^{(t)}}) = {P_1}{e^{{alpha _1}z}} + {P_2}{e^{{alpha _2}z}} + cdots + {P_m}{e^{{alpha _m}z}},$$

where n ≥ 3, t ≥ 0 and m ≥ 1 are integers, nm, P(z, f, f′, …, f(t)) is a differential polynomial in f (z) of degree dn with small functions of f (z) as its coefficients, and αj, Pj (j = 1, 2, …, m) are nonzero constants such that ∣α1∣ > ∣α2∣ > … > ∣αm∣. Also we provide the concrete forms of the solutions of the equation above, and present some examples illustrating the sharpness of our results.

利用亚纯函数的Nevanlinna理论,我们刻画了形式为$${f^n}{f^prime}+P(z,f,{f^prime},ldots,{f^(t)})={P_1}{e^{alpha_1}z}+{P_2}{e^{alpha_2}z}}+cdots+{P_m}{e^{[alpha_m}z}},$$的非线性微分方程的亚纯解,其中n≥3,t≥0和m≥1是整数,n≥m,P(z,f,f′,…,f(t))是f(z)中d≤n次的微分多项式,其系数为f(zα2Ş>>;⑪αmŞ。此外,我们还提供了上述方程解的具体形式,并举例说明了我们结果的清晰度。
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引用次数: 0
Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G) 群代数上某些Banach右模的射影性ℓ1(G)
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0234-2
S. Soltani Renani, Z. Yari

Let G be a locally compact group, ({cal B}({L^2}(G))) be the space of all bounded linear operators on L2(G), and (({cal T}({L^2}(G)), ast)) be the Banach algebra of trace class operators on L2(G). In this paper, we focus on some Banach right submodules of ({cal B}({L^2}(G))) over the convolution algebras (({cal T}({L^2}(G)), ast)) and (L1(G),*). We will see that if the locally compact group G is discrete, then the Banach right 1(G)-module structures of them are derived from their Banach right ({cal T}({ell ^2}(G)))-module structures. We also study the projectivity of these Banach right 1(G)-modules.

设G是一个局部紧群,({cal B}({L^2}(G)))是L2(G)上所有有界线性算子的空间,({cal T}(}L^2}(G),ast))是L2上迹类算子的Banach代数。本文研究了卷积代数(({cal T}({L^2}(G)),ast)和(L1(G),*)上的一些Banach右子模。我们将看到,如果局部紧致群G是离散的,那么Banach右ℓ它们的1(G)-模结构是从它们的Banach右({cal T}({ell^2}(G))-模构造导出的。我们还研究了这些Banach权的投影性ℓ1(G)-模块。
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引用次数: 0
Completion Procedures in Measure Theory 测量理论中的完成程序
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0233-3
A. G. Smirnov, M. S. Smirnov

We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content μ. With every such ring ({cal N}), an extension of μ is naturally associated which is called the ({cal N})-completion of μ. The ({cal N})-completion operation comprises most previously known completion-type procedures and also gives rise to some new extensions, which may be useful for constructing counterexamples in measure theory. We find a condition ensuring that σ-additivity of a content is preserved under the ({cal N})-completion and establish a criterion for the ({cal N})-completion of a measure to be again a measure.

我们提出了通过添加新的空集来统一处理群值内容的扩展(即定义在环上的加性集函数)。我们的方法基于内容μ的完备环的概念。对于每一个这样的环({cal N}),μ的一个扩展是自然关联的,它被称为μ的({cal N{)-完备。完备运算包含了大多数以前已知的完备型过程,也产生了一些新的扩展,这可能有助于构造测度论中的反例。我们发现了一个条件,确保一个内容的σ-可加性在({cal N})-完备下保持,并建立了一个测度的({{cl N})-完备再次是测度的标准。
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引用次数: 0
Stability of ({cal A}{cal N})-Operators under Functional Calculus 函数微积分下({cal A}{cl N})-算子的稳定性
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0231-5
G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki

In this note we discuss absolutely norm attaining property (({cal A}{cal N})-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the ({cal A}{cal N})-property under the functional calculus. As a consequence we discuss the operator mean of positive ({cal A}{cal N})-operators.

在这个注记中,我们讨论了Jordan乘积和李括号的绝对范数获得性质(({cal A}{cl N})-简言之性质)。我们提出了一个正绝对范数实现算子的函数演算,并讨论了函数演算下({cal a}{cl N})-性质的稳定性。因此,我们讨论了正算子的算子均值。
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引用次数: 0
On the Edrei–Goldberg–Ostrovskii Theorem for Minimal Surfaces 关于极小曲面的Edrei-Goldberg-Ostrovskii定理
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0230-6
A. Kowalski, I. I. Marchenko

This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein’s T*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.

本文致力于贝肯巴赫亚纯极小曲面理论的发展。我们考虑亚纯极小曲面的分离极大点的个数与Baernstein的T*-函数之间的关系。推广了Edrei、Goldberg、Heins、Ostrovski、Wiman的结果。我们还举例说明了所获得的估计是尖锐的。
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引用次数: 0
Building Blocks in Function Spaces 功能空间中的构建块
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-05 DOI: 10.1007/s10476-023-0236-0
H. Triebel

The spaces A sp,q (ℝn)with A ∈ {B, F}, s ∈ ℝ and 0 <p,q ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces A sp,q (ℝn) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions fS′(ℝn).

当A∈{B, F}, s∈∈,且0 <p,q≤∞时,空间A sp,q(∈n)通常用傅里叶解析分解的形式引入。以原子和小波为基础的相关表征,如今已相当彻底地为人所知。夸克使原子原子化,形成有建设性的构件。本研究的主要目的是将夸克分解提升到与空间A sp,q (v n)在原子或小波方面的相关表示相同的水平,最终达到缓和分布f∈S ' (v n)的普遍框架表示。
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引用次数: 0
Weighted Weak Type Mixed Φ-Inequalities for Martingale Maximal Operator 鞅极大算子的加权弱型混合Φ-不等式
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-05 DOI: 10.1007/s10476-023-0237-z
Y. Ren
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引用次数: 0
A Note on the Maximal Operator on Weighted Morrey Spaces 关于加权Morrey空间上最大算子的一个注记
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2023-09-05 DOI: 10.1007/s10476-023-0235-1
A. K. Lerner

In this paper we consider weighted Morrey spaces ({cal M}_{lambda ,{cal F}}^p(w)) adapted to a family of cubes ({cal F}), with the norm

$$Vert fVert{_{{cal M}_{lambda ,{cal F}}^p(w)}}: = mathop {sup }limits_{Q in {cal F}} {left( {{1 over {|Q{|^lambda }}}int_Q {|f{|^p}w} } right)^{1/p}},$$

and the question we deal with is whether a Muckenhoupt-type condition characterizes the boundedness of the Hardy–Littlewood maximal operator on ({cal M}_{lambda ,{cal F}}^p(w)).

In the case of the global Morrey spaces (when ({cal F}) is the family of all cubes in ℝn) this question is still open. In the case of the local Morrey spaces (when ({cal F}) is the family of all cubes centered at the origin) this question was answered positively in a recent work of Duoandikoetxea and Rosenthal [2].

We obtain an extension of [2] by showing that the answer is positive when ({cal F}) is the family of all cubes centered at a sequence of points in ℝn satisfying a certain lacunary-type condition.

本文考虑了适用于一组立方体({cal F})的加权Morrey空间({cal M}_{lambda ,{cal F}}^p(w)),其范数为$$Vert fVert{_{{cal M}_{lambda ,{cal F}}^p(w)}}: = mathop {sup }limits_{Q in {cal F}} {left( {{1 over {|Q{|^lambda }}}int_Q {|f{|^p}w} } right)^{1/p}},$$,我们处理的问题是在({cal M}_{lambda ,{cal F}}^p(w))上是否存在muckenhoudt型条件表征Hardy-Littlewood极大算子的有界性。对于全局Morrey空间(当({cal F})是所有立方体的族),这个问题仍然是开放的。在局部Morrey空间的情况下(({cal F})是所有以原点为中心的立方体的族),这个问题在duoanddikoetxea和Rosenthal bbb最近的工作中得到了肯定的回答。我们通过证明当({cal F})是满足一定空间型条件的以点序列为中心的所有立方体的族时,答案是正的,从而得到[2]的扩展。
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Analysis Mathematica
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