Volterra-type operators mapping weighted Dirichlet space into H^∞

2022/11/07 by José Ángel Peláez, Jouni Rättyä, Peláez, José Ángel +3
Mathematics · #30H20 #47B35 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2211.03351

openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The problem of describing the analytic functions g on the unit disc such that the integral operator T_g(f)(z)=∫₀^zf(ζ)g'(ζ) dζ is bounded (or compact) from a Banach space (or complete metric space) X of analytic functions to the Hardy space H^∞ is a tough problem and remains unsettled in many cases. For analytic functions g with non-negative Maclaurin coefficients, we describe the boundedness and compactness of T_g acting from a weighted Dirichlet space D^p_ω, induced by an upper doubling weight ω, to H^∞. We also characterize, in terms of neat conditions on ω, the upper doubling weights for which T_g: D^p_ω→ H^∞ is bounded (or compact) only if g is constant.

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