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

Abstract

For analytic functions g on the unit disk with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator Tg( f )(z) = z 0 f (ζ )g(ζ ) dζ from a space X of analytic functions in the unit disk to H∞, 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 Dp p−1, as well as the classical Bloch and BMOA spaces.