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http://hdl.handle.net/2445/9174
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 http://dx.doi.org/10.1155/S107379280413033X |
It is part of: | International Mathematics Research Notices, 2004, vol. 2004, núm. 19, p. 937-981. |
URI: | http://hdl.handle.net/2445/9174 |
Related resource: | http://dx.doi.org/10.1155/S107379280413033X |
ISSN: | 1073-7928 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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File | Description | Size | Format | |
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514784.pdf | 396.77 kB | Adobe PDF | View/Open |
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