首页/论文/1902.04786

arXiv 1902.047862019-02-13math.FA

The Kolmogorov-Riesz Theorem and Some Compactness Criterions of Bounded Subsets in Weighted Variable Exponent Amalgam and Sobolev Spaces

Ismail Aydin, Cihan Unal

备注：: 18 pages
DOI：: 10.1007/s13348-019-00262-5

英文摘要：

We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

The Amalgamation Property in Classical Lebesgue-Riesz Spaces, Banach Spaces with Transitive and Almost Transitive Norms and Projection Constants

In the article is shown that classes of finite equivalence that are generated by Lebesgue-Riesz spaces Lp have the amalgamation property if and only if p is not equal to an even natural number that is strongly large then 2.

2002-11-12math.FA

An improvement of the Kolmogorov-Riesz compactness theorem

The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.

2019-03-21math.FA

Boundedness of some operators on weighted amalgam spaces

Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical operators in harmonic analysis, such as the Hardy--Littlewood maximal operator, the Calderón--Zygmund operator, the Riesz potential, singular integral operators with the rough kernel, the Marcinkiewicz integral, the Bochner-Riesz operator, the Littlewood-Paley $g$ function and the intrinsic square function, are considered. Our main method is extrapolation. We obtai…

2021-10-04math.FA

Kolmogorov-Riesz紧性在渐近$L_p$空间中的扩展

Kolmogorov$\unicode{x2013}$Riesz compactness in asymptotic $L_p$ spaces

University of Vienna（维也纳大学）

本文将经典的Kolmogorov-Riesz紧性定理扩展到渐近$L_p$空间中，引入了额外的几乎等界条件，以刻画相对紧性。

2026-03-03math.FA

Dual of Hardy-amalgam spaces and norms inequalities

We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces, we prove that some classical linear operators such as Calderón-Zygmund, convolution and Riesz potential operators are bounded.

2018-10-03math.FA

The Kolmogorov-Riesz compactness theorem

We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.

2010-01-04math.CAmath.FA

更多相关论文收起更多论文

函数空间中的Riesz-Kolmogorov型紧性准则及其应用

Riesz-Kolmogorov type compactness criteria in function spaces with applications

本文提出适用于多种函数空间的Riesz-Kolmogorov型紧性准则，并用于刻画Bergman空间上的紧Toeplitz算子及推导Hardy空间上Hankel算子的紧性。

2022-04-29math.APmath.CAmath.CV

Compactness criteria for Stieltjes function spaces and applications

In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli-Arzelà and Kolmogorov-Riesz theorems, as well as their applications to Stieltjes-Sobolev spaces and decomposable functions.

2022-11-14math.FA

渐近 $L_p$ 空间中紧性的截断准则

A truncation criterion for compactness in asymptotic $L_p$ spaces

King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）

针对任意测度空间上的渐近 $L_p$ 空间，通过几乎等有界性与所有截断在 $L_p$ 中的全有界性刻画紧性，并简化了 $\mathbb R^n$ 上 Kolmogorov–Riesz 紧性定理的证明。

2026-06-16math.FA

加权Riesz-Kolmogorov准则与变指数Lebesgue空间上紧性的多线性外推

Compact sets in quasi-Banach function spaces and multilinear extrapolation of compactness on $L^{p(\cdot)}(w)$

Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Rheinische Friedrich-Wilhelms-Universität Bonn（波恩大学）

本文通过建立加权Riesz-Kolmogorov定理，在变指数Lebesgue空间上实现了多线性紧算子的外推，并得到了交换子、分数次积分和Fourier乘子的新加权紧性估计。

2026-09-21math.CAmath.FA

齐次型空间上的Banach格中的紧集

Compact sets in Banach lattices over spaces of homogeneous type

Ankara University（安卡拉大学）；Institute of Mathematics of the Academy of Sciences of the Czech Republic（捷克科学院数学研究所）；Chuo University（中央大学）

本文证明了齐次型空间上Banach格的Kolmogorov-Riesz紧性定理，用有界性、紧性和平均算子逼近刻画紧性，无需Vitali覆盖等假设，并推广至重排不变空间和Morrey空间。

2026-09-23math.APmath.CAmath.FA

粗糙奇异积分交换子的紧性

Compactness of commutators of rough singular integrals

本文刻画粗糙奇异积分算子 T_Ω 交换子在双权非对角情形下的紧性，并利用矩阵权 Kolmogorov-Riesz 定理得到矩阵权紧性结果。

2025-03-14math.CAmath.FA

与 Riesz-Feller 型 Dirac 算子相关的 Paley-Wiener 型定理

Paley-Wiener Type Theorems associated to Dirac Operators of Riesz-Feller type

TU Bergakademie Freiberg（弗莱贝格矿业工业大学）；University of Aveiro（阿威罗大学）

本文在超复变量框架下研究 Riesz-Feller 型分数阶 Dirac 算子，利用实 Paley-Wiener 方法刻画 Fourier 支集与 Cauchy 问题指数型解的关系，并推广 Bernstein 空间结果。

2025-06-07math.CVmath.FA

Compactness Characterizations of Commutators on Ball Banach Function Spaces

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. Let $Ω$ be a Lipschitz function on the unit sphere of ${\mathbb R}^n$,which is homogeneous of degree zero and has mean value zero, and let $T_Ω$ be the convolutional singular integral operator with kernel $Ω(\cdot)/|\cdot|^n$. In this article, under the assumption that the Hardy--Littlewood maximal operator $\mathcal{M}$ is bounded on both $X$ and its associated space, the authors prove that the commutator $[b,T_Ω]$ is compact on $X$ if and only if $b\in{\rm CMO}({\mathbb R}^n)$. To achieve this, the authors mainly employ three key to…

2021-01-19math.APmath.CAmath.FA

具有固定锥形集中的Sobolev波前集的分布空间：紧性、光滑映射的拉回与补偿紧性定理

Spaces of distributions with Sobolev wave front in a fixed conic set: compactness, pullback by smooth maps and the compensated compactness theorem

本文为具有固定锥形集中Sobolev波前集的分布空间引入局部凸拓扑，推广拉回、紧性、伪微分算子连续性与Rellich引理，并应用于微局域缺陷测度与补偿紧性定理。

2024-08-20math.APmath.DGmath.FA