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arXiv · 1209.0594

Generalized Hilbert Operators

Petros Galanopoulos·Daniel Girela·José Ángel Peláez·Aristomenis Siskakis
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Abstract

If $g$ is an analytic function in the unit disc $\D $ we consider the generalized Hilbert operator $\hg$ defined by {equation*}\label{H-g} \mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt. {equation*} We study these operators acting on classical spaces of analytic functions in $\D $. More precisely, we address the question of characterizing the functions $g$ for which the operator $\hg $ is bounded (compact) on the Hardy spaces $H^p$, on the weighted Bergman spaces $A^p_\alpha $ or on the spaces of Dirichlet type $\mathcal D^p_\alpha $.

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Petros Galanopoulos, Daniel Girela, José Ángel Peláez, Aristomenis Siskakis. 2012-09-04. Generalized Hilbert Operators. https://doi.org/10.5186/aasfm.2014.3912

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