A Derivative-Hilbert operator acting on BMOA space

2024/11/10 by Huiling Chen, Chen, Huiling, Shanli Ye +1
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2411.06433

openalex publication_date 2024/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let μ be a positive Borel measure on the interval [0,1). The Hankel matrix H_μ=(μ_n,k)_{n,k≥ 0} with entries μ_n,k=μ_n+k, where μ_n=∫_[0,1)tⁿdμ(t), induces, formally, the Derivative-Hilbert operator DH_μ(f)(z)=∑_n=0^∞(∑_k=0^∞ μ_n,ka_k)(n+1)zⁿ , ~z∈ \mathbbD, where f(z)=∑_n=0^∞ a_nzⁿ is an analytic function in \mathbbD. We characterize the measures μ for which DH_μ is a bounded operator on BMOA space. We also study the analogous problem from the α-Bloch space B_α(α>0) into the BMOA space.

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