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arXiv · 1112.3849

Capacities associated with Calderón-Zygmund kernels

Vasilis Chousionis·Joan Mateu·Laura Prat·Xavier Tolsa
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Abstract

Analytic capacity is associated with the Cauchy kernel $1/z$ and the $L^\infty$-norm. For $n\in\mathbb{N}$, one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$, $1\le i\le 2$, $x=(x_1,x_2)\in\mathbb{R}^2$. The main result of this paper states that the capacities associated with the vectorial kernel $(K_1, K_2)$ are comparable to analytic capacity.

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BibTeXRIS

Vasilis Chousionis, Joan Mateu, Laura Prat, Xavier Tolsa. 2012-08-29. Capacities associated with Calderón-Zygmund kernels. https://arxiv.org/abs/1112.3849

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