Capacities associated with scalar signed Riesz kernels, and analytic capacity
Classical Analysis and ODEs
2014-03-13 v2
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.
Keywords
Cite
@article{arxiv.1004.2170,
title = {Capacities associated with scalar signed Riesz kernels, and analytic capacity},
author = {Joan Mateu and Laura Prat and Joan Verdera},
journal= {arXiv preprint arXiv:1004.2170},
year = {2014}
}
Comments
37 pages, ams.org