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Potential theory of signed Riesz Kernels: capacity and Hausdorff measure

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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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International Mathematics Research Notices, 2004, vol. 2004, núm. 19, p. 937-981.

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Potential theory of signed Riesz Kernels: capacity and Hausdorff measure