Czechoslovak Mathematical Journal, Vol. 71, No. 1, pp. 211-229, 2021
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 $1<p<\infty$.
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, levanan@qnu.edu.vn