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
收藏
页码：283 / 306
页数：24
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