Approximation in the Zygmund class

被引：3

作者：

Nicolau, Artur ^{[1
]}

Soler i Gibert, Odi ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Cerdanyola Del Valles 08193, Spain

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2020年 / 101卷 / 01期

关键词：

26A16; 26A24 (primary); BOUNDED MEAN-OSCILLATION; SPACES; BMO; CLOSURE;

D O I：

10.1112/jlms.12267

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the distance in the Zygmund class ?* to the subspace I( BMO ) of functions with distributional derivative with bounded mean oscillation. In particular, we describe the closure of I( BMO ) in the Zygmund seminorm. We also generalise this result to Zygmund measures on Rd. Finally, we apply the techniques developed in the article to characterise the closure of the subspace of functions in ?* that are also in the classical Sobolev space W1,p, for 1.

引用

页码：226 / 246

页数：21

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