Capacities associated with scalar signed Riesz kernels, and analytic capacity

Details Capacities associated with scalar signed Riesz kernels, and analytic capacity Capacities associated with scalar signed Riesz kernels, and analytic capacity

2010-04-13

arxiv.org/abs/1004.2170v1

Mathematics

Classical Analysis and ODEs

37 pages, ams.org

Scientific paper

The real and imaginari parts of the Cauchy kernel in the plane are scalar Riesz kernels of homogeneity -1. One can associate with each of them a natural notion of capacity related to bounded potentials. The main result of the paper asserts that these capacities are comparable to classical analytic capacity, thus stressing the real variables nature of analytic capacity. Higher dimensional versions of this result are also considered.

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