SOBOLEV CAPACITY AND HAUSDORFF MEASURES IN METRIC MEASURE SPACES

被引:0
作者
Costea, Serban [1 ]
机构
[1] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada
基金
芬兰科学院;
关键词
Sobolev capacity; Hausdorff measures; HARMONIC-FUNCTIONS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper studies the relative Sobolev p-capacity in proper metric measure spaces when 1 < p < infinity. We prove that, this relative Sobolev 7,,capacity is Choquet. In addition, if the space X is doubling, unbounded, admits a weak (1,p)-Poincare inequality and has an "upper dimension" Q for some p <= Q < infinity, then we obtain lower estimates of the relative Sobolev p-capacities in terms of the Hausdorff content associated with continuous and doubling gauge functions h satisfying the decay condition (1) integral(1)(0)(h(t)/t(Q)-p)(1/p)dt/t < infinity. This condition generalizes a well-known condition in R(n).
引用
收藏
页码:179 / 194
页数:16
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