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

Abstract

Smoothness of the Green functions for the complement of rarefied Cantor-type sets is described in terms of the function Φ(δ)=(1/log 1/δ) that gives the logarithmic measure of sets. Markov's constants of the corresponding sets are evaluated. © 2010 Springer Science+Business Media, LLC.