Czechoslovak Mathematical Journal, first online, pp. 1-19


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

Van An Le

Received June 10, 2019.   Published online September 16, 2020.

Abstract:  We study Carleson measures and 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 disk of $\mathbb{C}$ to the unit ball of $\mathbb{C}^n$. 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 $1<p<\infty$.
Keywords:  Bergman space; Carleson measure; Toeplitz operator; Schatten classes
Classification MSC:  30H20, 47B35
DOI:  10.21136/CMJ.2020.0265-19

PDF available at:  Institute of Mathematics CAS

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Affiliations:   Van An Le, Aix-Marseille University, CNRS, Centrale Marseille, I2M, Marseille, France; University of Quynhon, Department of Mathematics and Statistics, 170 An Duong Vuong, Quy Nhon, Vietnam, e-mail: vanandkkh@gmail.com


 
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