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On Optimal Smoothness of the Green Function for the Complement of a Cantor-Type Set

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Constructive Approximation Aims and scope

Abstract

We give a new streamlined proof of a recent result by Totik concerning the local Holder 1/2 property of the Green function for the complement of a Cantor-type set taken with respect to the extended complex plane. To simplify the proof we find certain families of curves and estimate their moduli. In addition, we extend Totik's theorem to more general Cantor-type sets.

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  1. Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA

    V.V. Andrievskii

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  1. V.V. Andrievskii
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Correspondence to V.V. Andrievskii.

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Andrievskii, V. On Optimal Smoothness of the Green Function for the Complement of a Cantor-Type Set. Constr Approx 24, 113–122 (2006). https://doi.org/10.1007/s00365-005-0605-x

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  • DOI: https://doi.org/10.1007/s00365-005-0605-x

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