Composition operators from the Hardy space to the nth weighted-type space on the unit disk and the half-plane

摘要

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 the nth weighted-type space, where φ is an analytic self-map of X, is characterized.