Prat, Laura2009-08-202009-08-2020041073-7928https://hdl.handle.net/2445/9174In 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.45 p.application/pdfeng(c) Duke University Press, 2004Teoria del potencial (Matemàtica)Geometria algebraicaPotentials and capacitiesHausdorff and packing measuresinfo:eu-repo/semantics/article514784info:eu-repo/semantics/openAccess