Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem

IF 0.8 3区数学 Q2 MATHEMATICS

Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI:10.1007/s11464-021-0103-x

Shenyu Liu, Dongyong Yang, Ciqiang Zhuo

引用次数: 1

Abstract

In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight W is in the known Ap class, a characterization of totally bounded subsets in Lp(W) with p ∈ (1, ∞) is established.

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矩阵加权Kolmogorov-Riesz紧性定理

本文给出了具有矩阵权值的加权Lebesgue空间中Kolmogorov-Riesz紧性定理的几个版本。特别地，当矩阵权值W在已知的Ap类中时，建立了Lp(W)中p∈(1，∞)的全有界子集的刻画。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Frontiers of Mathematics in China MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

703

审稿时长

6-12 weeks

期刊介绍： Frontiers of Mathematics in China provides a forum for a broad blend of peer-reviewed scholarly papers in order to promote rapid communication of mathematical developments. It reflects the enormous advances that are currently being made in the field of mathematics. The subject areas featured include all main branches of mathematics, both pure and applied. In addition to core areas (such as geometry, algebra, topology, number theory, real and complex function theory, functional analysis, probability theory, combinatorics and graph theory, dynamical systems and differential equations), applied areas (such as statistics, computational mathematics, numerical analysis, mathematical biology, mathematical finance and the like) will also be selected. The journal especially encourages papers in developing and promising fields as well as papers showing the interaction between different areas of mathematics, or the interaction between mathematics and science and engineering.