NECESSARY CONDITIONS FOR WEIGHTED POINTWISE HARDY INEQUALITIES

被引：0
|
作者：
Lehrback, Juha [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland
来源：
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2009年 / 34卷 / 02期
基金：
芬兰科学院;
关键词：
Pointwise Hardy inequality; maximal function; Hausdorff content; Hausdorff dimension; Minkowski dimension;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish necessary conditions for domains Omega subset of R(n) which admit, the pointwise (p, beta)-Hardy inequality vertical bar u(x)vertical bar <= Cd(Omega)(x)(1-beta/p)M(2d Omega(x),q)(vertical bar del u parallel to d(Omega)(beta/p))(x), u is an element of C(0)(infinity)(Omega), where 1 < q < p, d(Omega)(x) = dist(x,partial derivative Omega), and M(R,q) is a maximal operator. In particular, the complement of such a domain must have. even locally, Hausdorff dimension strictly greater than n - p + beta.
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页码：437 / 446
页数：10
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