Sobolev spaces and hyperbolic fillings

被引：12

作者：

Bonk, Mario ^{[1
]}

Saksman, Eero ^{[2
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Box 95155, Los Angeles, CA 90095 USA

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

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2018年 / 737卷

基金：

芬兰科学院;

关键词：

QUASI-CONFORMAL MAPPINGS; POINCARE INEQUALITY;

D O I：

10.1515/crelle-2015-0036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Z be an Ahlfors Q-regular compact metric measure space, where Q>0. For p > 1 we introduce a new (fractional) Sobolev space A(p)(Z) consisting of functions whose extensions to the hyperbolic filling of Z satisfy a weak-type gradient condition. If Z supports a Q-Poincare inequality with Q > 1, then A(Q)(Z) coincides with the familiar ( homogeneous) Hajlasz-Sobolev space.

引用

页码：161 / 187

页数：27

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