Integral operators induced by symbols with non-negative Maclaurin coefficients mapping into $H^{\infty }$

Abstract

For analytic functions $g$ on the unit disc with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator $T_g(f)(z)={\int }_0^{z}f(\zeta )g^{\prime }(\zeta )d\zeta$ from a space $X$ of analytic functions in the unit disc 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 $D_{p-1}^p$, as well as the classical Bloch and BMOA spaces.