Self-improvement of uniform fatness revisited

被引：6

作者：

Lehrback, Juha ^{[1
]}

Tuominen, Heli ^{[1
]}

Vahakangas, Antti V. ^{[1
]}

机构：

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

来源：

MATHEMATISCHE ANNALEN | 2017年 / 368卷 / 3-4期

关键词：

HARDY INEQUALITIES; METRIC-SPACES; FAT SETS;

D O I：

10.1007/s00208-016-1431-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a new proof for the self-improvement of uniform p-fatness in the setting of general metric spaces. Our proof is based on rather standard methods of geometric analysis, and in particular the proof avoids the use of deep results from potential theory and analysis on metric spaces that have been indispensable in the previous proofs of the self-improvement. A key ingredient in the proof is a selfimprovement property for local Hardy inequalities.

引用

页码：1439 / 1464

页数：26

共 19 条

[1]

[Anonymous], 1993, OXFORD MATH MONOGR

[2]

[Anonymous], 1985, Sobolev Spaces

[3]

Bjorn A., 2011, TRACTS MATH, V17

[4] Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces [J].

Björn, J ;

MacManus, P ;

Shanmugalingam, N .

JOURNAL D ANALYSE MATHEMATIQUE, 2001, 85 (1) :339-369

[5] Orlicz-Hardy inequalities [J].

Buckley, SM ;

Koskela, P .

ILLINOIS JOURNAL OF MATHEMATICS, 2004, 48 (03) :787-802

[6] Differentiability of Lipschitz functions on metric measure spaces [J].

Cheeger, J .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 1999, 9 (03) :428-517

[7]

Hajlasz P, 2000, MEM AM MATH SOC, V145, pIX

[8] Quasiconformal maps in metric spaces with controlled geometry [J].

Heinonen, J ;

Koskela, P .

ACTA MATHEMATICA, 1998, 181 (01) :1-61

[9] The Poincare inequality is an open ended condition [J].

Keith, Stephen ;

Zhong, Xiao .

ANNALS OF MATHEMATICS, 2008, 167 (02) :575-599

[10] GLOBAL INTEGRABILITY OF THE GRADIENTS OF SOLUTIONS TO PARTIAL-DIFFERENTIAL EQUATIONS [J].

KILPELAINEN, T ;

KOSKELA, P .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (07) :899-909

← 1 2 →