Carleson measures and Toeplitz operators on small Bergman spaces on the ball. (English) Zbl 1524.30168
Summary: We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by K. Seip [Collect. Math. 64, No. 1, 61–72 (2013; Zbl 1266.30020)]. 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 \(1<p<\infty\).
MSC:
| 30H20 | Bergman spaces and Fock spaces |
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
Citations:
Zbl 1266.30020References:
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