Integral operators induced by symbols with non-negative Maclaurin coefficients mapping into H^∞

2021/03/16 by José Ángel Peláez, Jouni Rättyä, Peláez, José Ángel +3
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2103.09209

openalex publication_date 2021/03/16 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28

Abstract

For analytic functions g on the unit disc with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator T_g(f)(z)=∫₀^zf(ζ)g'(ζ) dζ from a space X of analytic functions in the unit disc to H^∞, in terms of neat and useful conditions on the Maclaurin coefficients of g. The choices of X that will be considered contain the Hardy and the Hardy-Littlewood spaces, the Dirichlet-type spaces D^p_p-1, as well as the classical Bloch and BMOA spaces.

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