Orlicz capacities and Hausdorff measures on metric spaces

Jana Björn, Jani Onninen

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided that ∫10Θ -1(t1-sh(t))dt< ∞ where Θ -1 is the inverse of the function Θ(t)=Φ(t)/t, and s is the "upper dimension" of the metric measure space. This condition is a generalization of a well known condition in R n . For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided.

Original languageEnglish (US)
Pages (from-to)131-146
Number of pages16
JournalMathematische Zeitschrift
Volume251
Issue number1
DOIs
StatePublished - Sep 1 2005
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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