Embedding theorems for a certain function class of Sobolev type on metric spaces

被引：2

作者：

Romanov, AS

机构：

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2004年 / 45卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

metric space; measure; Sobolev class; embedding theorem;

D O I：

10.1023/B:SIMJ.0000021292.79527.b5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a metric space with a Borel measure mu, we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p-summable with respect to mu. We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces.

引用

页码：376 / 387

页数：12

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