In between the inequalities of Sobolev and Hardy

被引：9

作者：

Lehrback, Juha ^{[1
]}

Vahakangas, Antti V. ^{[1
,2
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, FI-40014 Jyvaskyla, Finland

[2] Univ Helsinki, Dept Math & Stat, POB 68, FI-00014 Helsinki, Finland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2016年 / 271卷 / 02期

基金：

芬兰科学院;

关键词：

Sobolev inequality; Hardy inequality; Assouad dimension; DIMENSIONS; ASSOUAD; DOMAINS;

D O I：

10.1016/j.jfa.2016.04.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：330 / 364

页数：35

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