Integral operators mapping into the space of bounded analytic functions

Abstract

We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)={\int }_0^{z}f(\zeta )g^{\prime }(\zeta )d\zeta$ acting from a Banach space $X$ into $H^{\infty }$. We obtain a collection of general results which are appropriately applied and mixed with specific techniques in order to solve the posed questions to particular choices of $X$.