Toeplitz and Hankel products on Bergman spaces of the unit ball

Abstract

The authors give some new necessary conditions for the boundedness of Toeplitz products $T_f^\alpha T_{\bar g}^\alpha $ on the weighted Bergman space A _α ² of the unit ball, where f and g are analytic on the unit ball. Hankel products H _f H _g ^* on the weighted Bergman space of the unit ball are studied, and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.

Keywords

Weighted Bergman space / Unit ball / Toeplitz operator / Hankel operator / Berezin transform

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