Carleson measures and Toeplitz operators on small Bergman spaces on the ball

2018/09/18 by An Le, Le, An
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1809.06583

openalex publication_date 2018/09/18 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

We study the Carleson measures and the Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip's results from the unit disc of \mathbb C to the unit ball of \mathbb Cⁿ. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1

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