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Besov capacity and Hausdorff measures in metric measure spaces. (English) Zbl 1171.46025

Summary: This paper studies Besov \(p\)-capacities as well as their relationship to Hausdorff measures in Ahlfors regular metric spaces of dimension \(Q\) for \(1 < Q < p < \infty\). Lower estimates of the Besov \(p \)-capacities are obtained in terms of the Hausdorff content associated with gauge functions \(h\) satisfying the decay condition \(\int _0^1 h(t)^{1/(p-1)}\frac{dt}{t}< \infty\).

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31C99 Generalizations of potential theory
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