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Title: Potential theory of signed Riesz Kernels: capacity and Hausdorff measure
Author: Prat, Laura
Keywords: Teoria del potencial (Matemàtica)
Geometria algebraica
Potentials and capacities
Hausdorff and packing measures
Issue Date: 2004
Publisher: Duke University Press
Abstract: In this paper, we study the natural capacity γα related to the Riesz kernels x/∣x∣1 + α in ℝn, where 0 < α < n. For noninteger α, an unexpected behaviour arises: for 0 < α < 1, compact sets in ℝn with finite α-Hausdorff measure have zero γα capacity. In the Ahlfors-David regular case, for any noninteger index α, 0 < α < n, we prove that compact sets of finite α-Hausdorff measure have zero γα capacity.
Note: Reproducció del document publicat a
It is part of: International Mathematics Research Notices, 2004, vol. 2004, núm. 19, p. 937-981.
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ISSN: 1073-7928
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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