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2004

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/9174

Potential theory of signed Riesz Kernels: capacity and Hausdorff measure

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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.

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http://dx.doi.org/10.1155/S107379280413033X

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Teoria del potencial (Matemàtica), Geometria algebraica

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Potentials and capacities, Hausdorff and packing measures

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PRAT, Laura. Potential theory of signed Riesz Kernels: capacity and Hausdorff measure. International Mathematics Research Notices. 2004. Vol. 2004, num. 19, pags. 937-981. ISSN 1073-7928. [consulted: 6 of October of 2026]. Available at: https://hdl.handle.net/2445/9174

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