Integral operators mapping into the space of bounded analytic functions

2016/04/05 by Contreras, Manuel D., Peláez, José A., Pommerenke, Christian +1 · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1604.01214

Abstract

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) dζ 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.

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• Optimal domain of Volterra operators in classes of Banach spaces of analytic functions

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