Toeplitz operators via Carleson measures On β-modified Bergman Spaces

2023/10/05 by Safa Snoun, Snoun, Safa
Mathematics · Physics and Astronomy · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2310.03519

Abstract

In this paper, we study Bergman projection ℙ_α,β and Toeplitz operators T^α,β_φ on the β-modified Bergman space A_α,β^p. We give some properties of ℙ_α,β and a necessary and sufficient condition for T^α,β_φ to be compact. We end with a characterization of Toeplitz operators via Carleson measures by introducing a new Bergman metric inherited by the Bergman kernel \mathbbK_α,β that will be equivalent to the classical Bergman-Poincaré metric.

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