Singular operators with antisymmetric kernels, related capacities, and Wolff potentials

Details Singular operators with antisymmetric kernels, related capacities, and Wolff potentials Singular operators with antisymmetric kernels, related capacities, and Wolff potentials

2010-12-13

arxiv.org/abs/1012.2877v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for Calder\'on-Zygmund operators in metric spaces. We extend two versions of Calder\'on-Zygmund capacities in $R^d$ to metric spaces and establish their equivalence (under certain conditions). As an application, we extend the known relations between $s$-Riesz capacities, $0

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