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 C(phi)f(z) = f(phi(z)) from the Hardy space H-p (X), p > 0, where X is the upper half-plane Pi(+) = {z is an element of C : Imz > 0} or the unit disk D = {z is an element of C : vertical bar z vertical bar < 1} in the complex plane C, to the nth weighted-type space, where phi is an analytic self-map of X, is characterized.