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Potential theory of signed Riesz Kernels: capacity and Hausdorff measure Prat, Laura Teoria del potencial (Matemàtica) Geometria algebraica Potentials and capacities Hausdorff and packing measures 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. 2009-08-20T12:25:48Z 2009-08-20T12:25:48Z 2004 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 1073-7928 https://hdl.handle.net/2445/9174 514784 eng Reproducció del document publicat a http://dx.doi.org/10.1155/S107379280413033X International Mathematics Research Notices, 2004, vol. 2004, núm. 19, p. 937-981. http://dx.doi.org/10.1155/S107379280413033X (c) Duke University Press, 2004 info:eu-repo/semantics/openAccess 45 p. application/pdf Duke University Press Articles publicats en revistes (Matemàtiques i Informàtica)