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Keywords:
Bergman space; Carleson measure; Toeplitz operator; Schatten classes
Bergman space; Carleson measure; Toeplitz operator; Schatten classes
Summary:
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 $.
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