Carleson Measures and Toeplitz Operators on Small Bergman Spaces on the Ball

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 DOUBLE-STRUCK CAPITAL C to the unit ball of DOUBLE-STRUCK CAPITAL 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 < infinity.