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arXiv · 1809.06583

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

An Le
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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 $\mathbb C^n$. 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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An Le. 2018-09-18. Carleson measures and Toeplitz operators on small Bergman spaces on the ball. https://arxiv.org/abs/1809.06583

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