Composition Operators From The Hardy Space To Zygmund-type Spaces On The Upper Half-plane And The Unit Disc

Abstract

The paper characterizes the boundedness of the composition operator Cφf(z) = f(φ(z)) from the Hardy space Hp(X), p > 0, where X is the upper half-plane Π+ = {z ∈ C : Imz > 0} or the unit disk D = {z ∈ C : |z| < 1} in the complex plane C, to Zygmund-type spaces, where φ is an analytic selfmap of X.