On Ahlfors–Beurling Operator

Abstract

We investigate regularity properties of solutions of Beltrami equation expressed in terms of moduli of continuity. In particular, we prove that a class of Calderon–Zygmund operators, including Ahlfors–Beurling operator, preserves certain type of modulus of continuity of compactly supported functions. We also prove a purely topological result which easily gives injectivity of normal solutions of Beltrami equation.