Hilbert-type operator induced by radial weight on Hardy spaces

2022/07/29 by Noel Merchán, Merchán, Noel, José Ángel Peláez +3
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2207.14605

openalex publication_date 2022/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Hilbert-type operator defined by H_ω(f)(z)=∫₀¹ f(t)((1)/(z)∫₀^z B^ω_t(u) du) ω(t)dt, where \B^ω_ζ\_ζ∈\mathbbD are the reproducing kernels of the Bergman space A²_ω induced by a radial weight ω in the unit disc \mathbbD. We prove that H_ω is bounded on the Hardy space H^p, 1

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