Journal of Functional Analysis最新文献

英文中文

Duality, BMO and Hankel operators on Bernstein spaces 伯恩斯坦空间上的对偶性、BMO 和汉克尔算子

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-22 DOI: 10.1016/j.jfa.2024.110708

Carlo Bellavita , Marco M. Peloso

In this paper we deal with the problem of describing the dual space

{(B_{κ}^{1})}^{⁎}

of the Bernstein space

B_{κ}^{1}

, that is the space of entire functions of exponential type (at most)

κ > 0

whose restriction to the real line is Lebesgue integrable. We provide several characterizations, showing that such dual space can be described as a quotient of the space of entire functions of exponential type κ whose restriction to the real line are in a suitable BMO-type space, or as the space of symbols b for which the Hankel operator

H_{b}

is bounded on the Paley–Wiener space

B_{κ / 2}^{2}

. We also provide a characterization of

{(B_{κ}^{1})}^{⁎}

as the BMO space w.r.t. the Clark measures of the inner function

e^{i 2 κ z}

on the upper half-plane, in analogy with the known description of the dual of backward-shift invariant 1-spaces on the torus. Furthermore, we show that the orthogonal projection

P_{κ} : L^{2} (R) \to B_{κ}^{2}

induces a bounded operator from

L^{\infty} (R)

onto

{(B_{κ}^{1})}^{⁎}

Finally, we show that

B_{κ}^{1}

is the dual space of a suitable VMO-type space or as the space of symbols b for which the Hankel operator

H_{b}

on the Paley–Wiener space

B_{κ / 2}^{2}

is compact.

在本文中，我们讨论了描述伯恩斯坦空间 Bκ1 的对偶空间 (Bκ1)⁎ 的问题，即指数型（最多）κ>0 的全函数空间，其对实线的限制是 Lebesgue 可积分的。我们提供了几种描述，表明这种对偶空间可以被描述为指数型全函数 κ 空间的商，其对实线的限制是在合适的 BMO 型空间中，或描述为符号 b 的空间，其 Hankel 算子 Hb 在 Paley-Wiener 空间 Bκ/22 上是有界的。我们还提供了（Bκ1）⁎作为 BMO 空间的特征，即上半平面上内函数 ei2κz 的克拉克度量，这与已知的环上后移不变 1 空间对偶的描述类似。此外，我们还证明了正交投影 Pκ:L2(R)→Bκ2 从 L∞(R)到 (Bκ1)⁎ 引发了一个有界算子。最后，我们证明了 Bκ1 是一个合适的 VMO 型空间的对偶空间，或者是 Paley-Wiener 空间 Bκ/22 上的汉克尔算子 Hb 是紧凑的符号 b 空间。

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引用次数: 0

Sharp analytic version of Fefferman's inequality 费弗曼不等式的锐解析版本

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-22 DOI: 10.1016/j.jfa.2024.110707

Tomasz Gałązka, Adam Osękowski

Let

T

be a unit circle. Assume further that f is an element of the Hardy space

H^{1} (T)

and g belongs to the analytic BMO space on

T

. The paper contains the identification of the optimal universal constant C in the estimate

| \frac{1}{2 π} \int_{T} \overline{f (ζ)} g (ζ) d ζ | \leq C {‖ f ‖}_{H^{1} (T)} {‖ g ‖}_{B M O (T)} .

Actually, the inequality is studied in the stronger form, involving the Littlewood-Paley function on the left and the sharp maximal function of g on the right. The proof rests on the construction of an appropriate plurisuperharmonic function on a parabolic domain and the application of probabilistic techniques.

假设 T 是单位圆。本文包含对估计|12π∫Tf(ζ)‾g(ζ)dζ|≤C‖f‖H1(T)‖g‖BMO(T)中最优通用常数 C 的鉴定。实际上，不等式是以更强的形式研究的，左边涉及 Littlewood-Paley 函数，右边涉及 g 的尖锐最大函数。证明依赖于在抛物线域上构造一个适当的诸超谐函数以及概率技术的应用。

引用次数: 0

Hermite expansions for spaces of functions with nearly optimal time-frequency decay 具有近乎最佳时频衰减的函数空间的赫米特展开式

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-22 DOI: 10.1016/j.jfa.2024.110706

Lenny Neyt , Joachim Toft , Jasson Vindas

We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line satisfying

| f (x) | ≲ e^{- (\frac{1}{2} - λ) x^{2}}, | \hat{f} (ξ) | ≲ e^{- (\frac{1}{2} - λ) ξ^{2}}, \forall λ > 0 .

In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in [21]. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle.

我们为满足|f(x)|≲e-(12-λ)x2,|fˆ(ξ)|≲e-(12-λ)ξ2,∀λ>0的实线上函数的弗雷谢特空间的几个子空间建立了赫米特展开特性。特别是，我们扩展并改进了 [21] 中得到的所谓适当 Pilipović 空间的傅立叶特性。我们证明的主要内容是巴格曼变换和普拉格门-林德洛夫原理的一些最优形式。

引用次数: 0

Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow 能量临界兰道-利夫施齐兹流平稳等变解的胀破动力学

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-21 DOI: 10.1016/j.jfa.2024.110704

Jitao Xu, Lifeng Zhao

In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping

R^{2}

S^{2}

with arbitrary given coefficients

ρ_{1} \in R, ρ_{2} > 0

. We prove that there exists a codimension one smooth well-localized set of initial data arbitrarily close to the ground state which generates type-II finite-time blowup solutions, and give a precise description of the corresponding singularity formation. In our proof, both the Schrödinger part and the heat part play important roles in the construction of approximate solutions and the mixed energy/Morawetz functional. However, the blowup rate is independent of the coefficients.

本文研究了任意给定系数ρ1∈R,ρ2>0的能量临界一等变Landau-Lifschitz流映射R2到S2。我们证明了存在一个任意接近基态的一维光滑良好局部初始数据集，该数据集会产生 II 型有限时间炸毁解，并给出了相应奇点形成的精确描述。在我们的证明中，薛定谔部分和热量部分在近似解和混合能量/莫拉维兹函数的构造中都发挥了重要作用。然而，炸毁率与系数无关。

引用次数: 0

On the classification of function algebras on subvarieties of noncommutative operator balls 论非交换算子球子变量上的函数代数分类

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-18 DOI: 10.1016/j.jfa.2024.110703

Jeet Sampat, Orr Moshe Shalit

We study algebras of bounded noncommutative (nc) functions on unit balls of operator spaces (nc operator balls) and on their subvarieties. Considering the example of the nc unit polydisk we show that these algebras, while having a natural operator algebra structure, might not be the multiplier algebra of any reasonable nc reproducing kernel Hilbert space (RKHS). After examining additional subtleties of the nc RKHS approach, we turn to study the structure and representation theory of these algebras using function theoretic and operator algebraic tools. We show that the underlying nc variety is a complete invariant for the algebra of uniformly continuous nc functions on a homogeneous subvariety, in the sense that two such algebras are completely isometrically isomorphic if and only if the subvarieties are nc biholomorphic. We obtain extension and rigidity results for nc maps between subvarieties of nc operator balls corresponding to injective spaces that imply that a biholomorphism between homogeneous varieties extends to a biholomorphism between the ambient balls, which can be modified to a linear isomorphism. Thus, the algebra of uniformly continuous nc functions on nc operator balls, and even its restriction to certain subvarieties, completely determine the operator space up to completely isometric isomorphism.

我们研究算子空间单位球（nc 算子球）及其子域上的有界非交换（nc）函数代数。以 nc 单位多面体为例，我们发现这些代数虽然具有自然的算子代数结构，但可能不是任何合理的 nc 重现核希尔伯特空间（RKHS）的乘子代数。在考察了 nc RKHS 方法的其他微妙之处后，我们转而使用函数论和算子代数工具研究这些代数的结构和表示理论。我们证明了底层 nc 变项是均匀连续 nc 函数在同质子变项上的代数的完全不变项，也就是说，当且仅当子变项是 nc 双全等时，两个这样的代数完全同构。我们得到了 nc 算子球对应于注入空间的子变量之间的 nc 映射的扩展和刚度结果，这意味着同质变量之间的双全同性扩展为环境球之间的双全同性，而环境球之间的双全同性可以修正为线性同构。因此，nc 算子球上的均匀连续 nc 函数代数，甚至其对某些子变量的限制，都完全决定了算子空间的完全等距同构。

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引用次数: 0

Continuous asymmetric Doob inequalities in noncommutative symmetric spaces 非交换对称空间中的连续非对称 Doob 不等式

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-15 DOI: 10.1016/j.jfa.2024.110701

Yong Jiao, Hui Li, Sijie Luo, Lian Wu

<div><div>Let <math><mo>(</mo><mi>M</mi><mo>,</mo><mi>τ</mi><mo>)</mo></math> be a noncommutative probability space equipped with a filtration <math><msub><mrow><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></msub></math> whose union is <math><msup><mrow><mi>w</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>-dense in <math><mi>M</mi></math>, and let <math><msub><mrow><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></msub></math> be the associated conditional expectations. We prove in the present paper that if the symmetric space <math><mi>E</mi><mo>∈</mo><mi>Int</mi><mo>[</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>]</mo></math> with <math><mn>1</mn><mo><</mo><mi>p</mi><mo>≤</mo><mi>q</mi><mo><</mo><mn>2</mn></math> and E is <math><mn>2</mn><mo>(</mo><mn>1</mn><mo>−</mo><mi>θ</mi><mo>)</mo></math>-convex and w-concave with <math><mi>p</mi><mo><</mo><mi>w</mi><mo><</mo><mn>2</mn></math>, then the following holds:<math><msub><mrow><mo>‖</mo><msub><mrow><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></msub><mo>‖</mo></mrow><mrow><mi>E</mi><mo>(</mo><mi>M</mi><mo>;</mo><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>θ</mi></mrow></msubsup><mo>)</mo></mrow></msub><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>E</mi><mo>,</mo><mi>θ</mi></mrow></msub><msub><mrow><mo>‖</mo><mi>x</mi><mo>‖</mo></mrow><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>E</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow></msub><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi>E</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>(</mo><mi>M</mi><mo>)</mo></math> provided <math><mn>1</mn><mo>−</mo><mi>p</mi><mo>/</mo><mn>2</mn><mo><</mo><mi>θ</mi><mo><</mo><mn>1</mn></math>. Similar result holds for <math><mi>x</mi><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi>E</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><mi>M</mi><mo>)</mo></math>. Moreover, if <math><mi>E</mi><mo>∈</mo><mi>Int</mi><mo>[</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>]</mo></math> with <math><mn>1</mn><mo><</mo><mi>p</mi><mo>≤</mo><mi>q</mi><mo><</mo><mn>2</mn></math> and E is w-concave with <math><mn>2</

让（M,τ）是一个非交换概率空间，配备了一个滤波 (Mt)t∈[0,1]，其联合在 M 中是 w⁎密集的；让 (Et)t∈[0,1] 是相关的条件期望。本文将证明，如果对称空间 E∈Int[Lp,Lq]为 1<p≤q<2，且 E 为 2(1-θ)-convex 和 w-concave 为 p<w<2，则以下条件成立：Et（x））t∈[0，1]‖E（M；ℓ∞θ）≤CE，θ‖x‖HEc，x∈HEc（M）提供 1-p/2<；θ<；1。类似的结果也适用于 x∈HEr(M)。此外，如果 E∈Int[Lp,Lq]为 1<p≤q<2，且 E 为 w-concave with 2<w<；2p/(2-p)，则对于每个 x∈E(M)存在 y、z∈E(M)，使得 x=y+z 且‖(Et(y))t∈[0,1]‖E(M;ℓ∞c)+‖(Et(z))t∈[0,1]‖E(M;ℓ∞r)≤c‖Ex‖E(M)。这些结果可视为 Randrianantoanina 等人[33]的连续类似结果。我们证明的关键要素之一是一般对称空间 E 的 E(M)模块的新分解定理，它扩展了 Junge 和 Sherman 的已知结果。

引用次数: 0

Functional L1-Lp inequalities in the CAR algebra CAR 代数中的函数 L1-Lp 不等式

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-15 DOI: 10.1016/j.jfa.2024.110700

Yong Jiao, Sijie Luo, Dejian Zhou

In the present paper, we use the semigroup method to investigate various functional inequalities invoking

L_{1}

and

L_{p}

norms in the framework of canonical anti-commuting relations algebra (CAR algebra for short). As the main results, we obtain the Poincaré inequality for Talagrand type sum, Eldan-Gross inequality for projections, and the Talagrand influence inequality along with its strengthening form in the CAR algebra. All our results strengthen the noncommutative Poincaré inequality of Efraim and Lust-Piquard at several points. We conclude the paper with two applications of our inequalities. In the first application, we apply the noncommutative Eldan-Gross inequality to derive two KKL-type inequalities in the CAR algebra, which are closely related to the quantum KKL conjecture of Montanaro and Osborne. The second application is the CAR algebra counterpart of the superconcentration phenomenon derived from the noncommutative Talagrand influence inequality.

在本文中，我们使用半群方法研究了在典型反交换关系代数（简称 CAR 代数）框架内援引 L1 和 Lp 准则的各种函数不等式。作为主要结果，我们得到了塔拉格兰德型和的庞加莱不等式、投影的埃尔丹-格罗斯不等式和塔拉格兰德影响不等式及其在 CAR 代数中的加强形式。我们的所有结果都在若干点上加强了埃弗拉伊姆和卢斯特-皮夸德的非交换泊恩卡雷不等式。最后，我们以两个不等式的应用来结束本文。在第一个应用中，我们应用非交换埃尔丹-格罗斯不等式推导出 CAR 代数中的两个 KKL 型不等式，它们与蒙塔纳罗和奥斯本的量子 KKL 猜想密切相关。第二个应用是非交换塔拉格朗影响不等式推导出的 CAR 代数对应的超集中现象。

引用次数: 0

Inclusions of simple C⁎-algebras arising from compact group actions 由紧凑群作用产生的简单 C⁎-代数的夹杂物

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-15 DOI: 10.1016/j.jfa.2024.110702

Miho Mukohara

Inclusions of operator algebras have long been studied. In particular, inclusions arising from actions of compact groups on factors were studied by Izumi-Longo-Popa and others. The correspondence between intermediate subfactors and subgroups is called the Galois correspondence. Analogues for actions on C^⁎-algebras have been studied by Izumi, Cameron-Smith, Peligrad, and others. In this article, we give examples of compact group actions on simple C^⁎-algebras for which the Galois correspondence holds.

对算子代数的夹杂物的研究由来已久。特别是，Izumi-Longo-Popa 等人研究了紧凑群对因子的作用所产生的夹杂。中间子因子与子群之间的对应关系称为伽罗瓦对应关系。Izumi、Cameron-Smith、Peligrad 等人研究了 C⁎-代数上的类似作用。本文将举例说明伽罗瓦对应关系成立的简单 C⁎-代数上的紧凑群作用。

引用次数: 0

On dual Kadec norms 关于双卡德克规范

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-09 DOI: 10.1016/j.jfa.2024.110698

Petr Hájek

Let

(X, ‖ \cdot ‖)

be a Banach space such that all

w^{⁎}

-convergent sequences in the dual unit sphere

S_{X^{⁎}}

are also norm convergent. Then the weak^⁎ and norm topologies agree on

S_{X^{⁎}}

. By known results it implies that X has a renorming whose dual is locally uniformly rotund, hence also

C^{1}

-Fréchet smooth. In particular, X is an Asplund space. Our results also lend an alternative proof of the celebrated Josefson-Nissenzweig theorem.

设（X,‖⋅‖）是一个巴拿赫空间，其对偶单位球 SX⁎中所有 w⁎ 收敛序列也是规范收敛的。那么弱⁎拓扑和规范拓扑在 SX⁎上是一致的。根据已知结果，这意味着 X 有一个重重整，其对偶是局部均匀旋转的，因此也是 C1-弗雷谢特光滑的。特别是，X 是一个阿斯普朗德空间。我们的结果还为著名的约瑟夫森-尼森茨威格定理提供了另一种证明。

引用次数: 0

Imprimitivity theorems and self-similar actions on Fell bundles 费尔束上的本构定理和自相似作用

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-09 DOI: 10.1016/j.jfa.2024.110699

Anna Duwenig , Boyu Li

We introduce the notion of self-similar actions of groupoids on other groupoids and Fell bundles. This leads to a new imprimitivity theorem arising from such dynamics, generalizing many earlier imprimitivity theorems involving group and groupoid actions.

我们引入了类群对其他类群和费尔束的自相似作用的概念。这引出了由这种动力学产生的一个新的蕴涵性定理，概括了早期许多涉及群和群实体作用的蕴涵性定理。

引用次数: 0

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