COMPOSITION OPERATORS FROM THE HARDY SPACE TO ZYGMUND-TYPE SPACES ON THE UPPER HALF-PLANE AND THE UNIT DISC

摘要

The paper characterizes 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 : Im z > 0} or the unit, disk D= {z is an element of C : vertical bar z vertical bar < 1} in the complex plane C, to Zygmund-type spaces, where phi is an analytic self-map of X.