Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space

2018/05/30 by Songxiao Li, Li, Songxiao, Jizhen Zhou +1
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1805.11967

openalex publication_date 2018/05/30 · 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 induces the operator H_μ(f)(z)=∑^∞_n=0(∑^∞_k=0μ_n,ka_k)zⁿ on the space of all analytic functions f(z)=∑^∞_n=0a_nzⁿ in the unit disk \mathbbD. In this paper, we characterize the boundedness and compactness of H_μ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of H_μ from α Bloch type spaces to Bloch space and BMOA.

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