Restricted Beurling transforms on Campanato spaces

Abstract

Let Ω ⊂ C be a bounded domain with C 1,ω -smooth boundary, where ω is a Dini-smooth modulus of continuity. We prove that the restricted Beurling transform is bounded on the Campanato space BMOω(Ω).2010 Mathematics Subject Classification. Primary 42B20; Secondary 30C62, 30H30, 46E15.

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