Generalized Hilbert matrix operators acting on Bergman spaces

2024/07/18 by Carlo Bellavita, Bellavita, Carlo, Vassilis Daskalogiannis +9 · 1 citation
Mathematics · Computer Science · #Advanced Topics in Algebra #Holomorphic and Operator Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2407.13569

Abstract

In this article we study the generalized Hilbert matrix operator Γ_μ acting on the Bergman spaces A^p of the unit disc for 1≤ p<∞. In particular, we characterize the measures μ for which the operator Γ_μ is bounded and we provide estimates of its operator norm. Finally, we also describe when Γ_μ is compact by computing its essential norm.

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