Integral operators mapping into the space of bounded analytic functions
  We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ 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 $X$. 
Manuel D. Contreras, Jos\'e A. Pel\'aez, Christian Pommerenke and   Jouni R\"atty\"a
math.FA math.CV