Integral operators mapping into the space of bounded analytic functions

By Manuel D. Contreras, J. A. Pel'aez, C. Pommerenke, Jouni Rattya. 2016

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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 $X$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/261b4e9f12393b2fde97aa7b4fa35eda05201d3a