A generalized Hilbert matrix acting on Hardy spaces

2013/09/24 by Christos Chatzifountas, Chatzifountas, Christos, Daniel Girela +3 · 3 citations
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.1309.6125

arxiv created 2013/09/24 · arxiv updated 2013/09/25

Abstract

If μ is a positive Borel measure on the interval [0, 1), the Hankel matrix \mathcal H_μ=(μ_n,k)_{n,k≥ 0} with entries μ_n,k=∫_[0,1)t^n+k dμ(t) induces formally the operator H_μ(f)(z)=∑_n=0^∞(∑_k=0^∞μ_n,ka_k)zⁿ on the space of all analytic functions f(z)=∑_k=0^∞ a_kz^k, in the unit disc \mathbbD . In this paper we describe those measures μ for which H_μ is a bounded (compact) operator from H^p into H^q, 0<p,q<∞ . We also characterize the measures μ for which \mathcal H_μ lies in the Schatten class S_p(H²), 1<p<∞.

Cited by

• Cesàro-type operators on mixed norm spaces
• Cesàro-type operators acting on Dirichlet spaces
• Generalized Hilbert operators acting from Hardy spaces to weighted Bergman spaces

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