Compactness in the spaces of functions of bounded variation

被引：0

作者：

Gulgowski, Jacek ^{[1
]}

机构：

[1] Univ Gdansk, Inst Math, Fac Math Phys & Informat, PL-80308 Gdansk, Poland

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2023年 / 42卷 / 3-4期

关键词：

Bounded variation; Waterman variation; Young variation; integral variation; compactness; BV;

D O I：

10.4171/ZAA/1733

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, the characterization of the compactness in the space BV ([0, 1]) of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman Lambda-variation, Young phi-variation and integral variation. It appears that, on the compact sets, the norm is uniformly approximated by certain seminorms induced by the selection of finitely many intervals in [0, 1].

引用

页码：283 / 306

页数：24

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