Bounded Hankel Products on the Bergman Space of the Polydisk

http://dx.doi.org/10.4153/CJM-2009-009-0
Canad. J. Math. 61(2009), 190-204

  Published:2009-02-01
 Printed: Feb 2009

We consider the problem of determining for which square integrable functions $f$ and $g$ on the polydisk the densely defined Hankel product $H_{f}H_g^\ast$ is bounded on the Bergman space of the polydisk. Furthermore, we obtain similar results for the mixed Haplitz products $H_{g}T_{\bar{f}}$ and $T_{f}H_{g}^{*}$, where $f$ and $g$ are square integrable on the polydisk and $f$ is analytic.