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Integral operators mapping into the space of bounded analytic functions

2016; Elsevier BV; Volume: 271; Issue: 10 Linguagem: Inglês

10.1016/j.jfa.2016.05.021

1096-0783

Manuel D. Contreras, José Ángel Peláez, Christian Pommerenke, Jouni Rättyä,

Analytic and geometric function theory

We address the problem of studying the boundedness, compactness and weak compactness of the integral operators T g ( f ) ( z ) = ∫ 0 z f ( ζ ) g ′ ( ζ ) d ζ acting from a Banach space X into H ∞ . 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 .