Abstract
Analytic capacity is associated with the Cauchy kernel 1/z and the L ∞-norm. For n ∈ ℕ, one has likewise capacities related to the kernels \(K_i(x)=x_i^{2n-1}/|x|^{2n}\), 1 ≤ i ≤ 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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Most of this work had been carried out in the first semester of 2011 while V.C was visiting the Centre de Recerca Matemàtica in Barcelona and he feels grateful for the hospitality. V.C was supported by the Academy of Finland. J.M and L.P are supported by grants 2009SGR-000420 (Generalitat de Catalunya) and MTM2010-15657 (Spain). X.T is supported by grants 2009SGR-000420 (Generalitat de Catalunya) and MTM2010-16232 (Spain).
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Chousionis, V., Mateu, J., Prat, L. et al. Capacities Associated with Calderón-Zygmund Kernels. Potential Anal 38, 913–949 (2013). https://doi.org/10.1007/s11118-012-9301-1
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DOI: https://doi.org/10.1007/s11118-012-9301-1