On the Modulus of Continuity of Weakly Differentiable Functions

被引：16

作者：

Cianchi, Andrea ^{[1
]}

Randolfi, Monia ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, I-50122 Florence, Italy

[2] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2011年 / 60卷 / 06期

关键词：

generalized Sobolev spaces; rearrangement invariant spaces; modulus of continuity; Orlicz-Sobolev spaces; SOBOLEV EMBEDDINGS; INEQUALITIES; OPERATORS; SPACES;

D O I：

10.1512/iumj.2011.60.4441

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Optimal embeddings of Sobolev type spaces into spaces of continuous functions are established. On extending the classical Morrey embedding on the Holder continuity of functions with weak derivatives in suitable Lebesgue spaces, our results provide the sharp modulus of continuity of functions whose weak derivatives of a given order belong to a more general rearrangement invariant space. In particular, embeddings of Orlicz-Sobolev spaces into spaces of continuous functions are characterized.

引用

页码：1939 / 1973

页数：35

共 29 条

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