A Dual Characterization of the C1 Harmonic Capacity and Applications
نویسندگان
چکیده
The Lipschitz and C harmonic capacities κ and κc in R n can be considered as high-dimensional versions of the so-called analytic and continuous analytic capacities γ and α (respectively). In this paper we provide a dual characterization of κc in the spirit of the classical one for the capacity α by means of the Garabedian function. Using this new characterization, we show that κ(E) = κ(∂oE) for any compact set E ⊂ R, where ∂oE is the outer boundary of E, and we solve an open problem posed by A. Volberg, which consists on estimating from below the Lipschitz harmonic capacity of a graph of a continuous function.
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