New characterizations of Hajlasz-Sobolev spaces on metric spaces

被引：76

作者：

Yang, DC ^{[1
]}

机构：

[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2003年 / 46卷 / 05期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

Sobolev space; Lipschitz-type space; embedding theorem; maximal function; space of homogeneous type;

D O I：

10.1360/02ys0343

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper introduces the fractional Sobolev spaces on spaces of homogeneous type, including metric spaces and fractals. These Sobolev spaces include the well-known Hajlasz-Sobolev spaces as special models. The author establishes various characterizations of (sharp) maximal functions for these spaces. As applications, the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces. Moreover, some embedding theorems are also given.

引用

页码：675 / 689

页数：15

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