Conformal mappings of domains satisfying a wedge condition

Abstract

A plane Jordan curve F satisfies an interior (exterior) wedge condition if for some a s (0,1) there is a fixed wedge of opening ait such that for any u> e T one may place a wedge inside (outside) F with vertex at u. Let /be a conformai mapping of the disk D onto the interior of T. We establish Holder continuity of/(/"') on 3D( T) with best possible exponents in terms of a.