Compactness in Lipschitz spaces and around

IF 0.7 3区数学 Q2 MATHEMATICS Studia Mathematica Pub Date : 2022-05-09 DOI:10.4064/sm221020-16-3

J. Gulgowski, P. Kasprzak, Piotr Ma'ckowiak

引用次数: 1

Abstract

The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces needed to be established. Those auxiliary results, which are interesting on their own since they use a concept of equicontinuity not seen in the literature, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.

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Lipschitz空间及其周围的紧性

本文的目的是刻画Lipschitz/H空间中的（预）紧性\从紧致度量空间到赋范空间的较老的连续映射。为此，需要对赋范空间中有值的有界和连续映射的空间的现有紧致性标准进行一些扩展和推广。这些辅助结果本身就很有趣，因为它们使用了在L中看不到的等连续性概念ature是基于与最近引入的二分形式集合的概念相关的抽象紧致性准则。

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

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.

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