Abstract

Let G be a bounded plane domain whose boundary consists of finitely many disjoint quasicircles. Let u be a harmonic in G and continuous in \(\bar G\),the closure of G. We assume that the modulus of continuity of u is majorized by a suitable type of function on the boundary of G and obtain estimates for the modulus of continuity ofuin\(\bar G\).We show by examples that in a certain sense these estimates are best possible.

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