Capacities Associated with Calderón-Zygmund Kernels

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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 Ki(x)=xi2n-1/{pipe}x{pipe}2n, 1 ≤ i ≤ 2, x = (x1, x2) ∈ ℝ2. The main result of this paper states that the capacities associated with the vectorial kernel (K1, K2) are comparable to analytic capacity. © 2012 Springer Science+Business Media B.V.
Original languageEnglish
Pages (from-to)913-949
JournalPotential Analysis
Publication statusPublished - 1 Jan 2013


  • Analytic capacity
  • Calderón-Zygmund kernels


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