Generalized Hilbert Operator Acting on Hardy Spaces

2024/10/27 by Huiling Chen, Chen, Huiling, Shanli Ye +1
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2410.20435

Abstract

Let α>0 and μ be a positive Borel measure on the interval [0,1). The Hankel matrix H_μ,α=(μ_n,k,α)_n,k≥0 with entries μ_n,k,α=∫_[0,1)(Γ(n+α))/(Γ(n+1)Γ(α))t^n+kdμ(t), induces, formally, the generalized-Hilbert operator as H_μ,α ( f ) ( z ) =∑_n=0^∞ (∑_k=0^∞ μ_n,k,αa_k )zⁿ,z∈\mathbbD where f(z)=\textstyle ∑_k=0^∞ a_kz^k is an analytic function in \mathbbD. This article is devoted study the measures μ for which H_μ,α is a bounded(resp., compact) operator from H^p(0

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