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 language | English (US) |
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Pages (from-to) | 131-146 |
Number of pages | 16 |
Journal | Mathematische Zeitschrift |
Volume | 251 |
Issue number | 1 |
DOIs | |
State | Published - Sep 2005 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)