Integral Operators Induced by Symbols with Non-negative Maclaurin Coefficients Mapping into H^infty

Abstract

For analytic functions g on the unit disk with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator T_g(f)(z)=int _0^zf(zeta )g'(zeta ),dzeta from a space X of analytic functions in the unit disk to H^infty , in terms of neat and useful conditions on the Maclaurin coefficients of g. The choices of X that will be considered contain the Hardy and the Hardy–Littlewood spaces, the Dirichlet-type spaces D^p_{p-1}, as well as the classical Bloch and mathord {mathrm{BMOA}} spaces.