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

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) = integral(z)(0) f (zeta)g'(zeta) d zeta from a space X of analytic functions in the unit disk to H-infinity, 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-1(p), as well as the classical Bloch and BMOA spaces.