Geodesic
Carleson measures and Toeplitz operators on small Bergman spaces on the ball
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 211-229

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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 $1$.
DOI : 10.21136/CMJ.2020.0265-19
Classification : 30H20, 47B35
Keywords: Bergman space; Carleson measure; Toeplitz operator; Schatten classes 
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Le, Van An. Carleson measures and Toeplitz operators  on small Bergman spaces on the ball. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 211-229. doi: 10.21136/CMJ.2020.0265-19

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