The equivalence between pointwise Hardy inequalities and uniform fatness

Riikka Korte, Juha Lehrbäck, Heli Tuominen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

17 Citations (Scopus)

Abstract

We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean spaces, but our methods apply in general metric spaces as well. We also present a new transparent proof for the fact that uniform capacity density implies the classical integral version of the Hardy inequality in the setting of metric spaces. In addition, we consider the relations between the above concepts and certain Hausdorff content conditions.

Original languageEnglish
Pages (from-to)711-731
Number of pages21
JournalMATHEMATISCHE ANNALEN
Volume351
Issue number3
DOIs
Publication statusPublished - 1 Nov 2011
MoE publication typeA1 Journal article-refereed

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