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arXiv · 1004.2170

Capacities associated with scalar signed Riesz kernels, and analytic capacity

Joan Mateu·Laura Prat·Joan Verdera
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Abstract

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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Joan Mateu, Laura Prat, Joan Verdera. 2014-03-12. Capacities associated with scalar signed Riesz kernels, and analytic capacity. https://arxiv.org/abs/1004.2170

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