Hardy-Sobolev inequalities and weighted capacities in metric spaces
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Published:2022-12-04
Issue:3
Volume:128
Page:
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ISSN:1903-1807
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Container-title:MATHEMATICA SCANDINAVICA
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language:
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Short-container-title:Math. Scand.
Author:
Ihnatsyeva Lizaveta,Lehrbäck Juha,Vähäkangas Antti V.
Abstract
Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy–Sobolev inequality in $\Omega$ and quasiadditivity of a weighted capacity with respect to Whitney covers of $\Omega$. Important ingredients in the proof include the use of a discrete convolution as a capacity test function and a Maz'ya type characterization of weighted Hardy–Sobolev inequalities.
Publisher
Det Kgl. Bibliotek/Royal Danish Library
Subject
General Mathematics