Bounded Toeplitz and Hankel productson weighted Bergman spaces of the unit ball
Volume 99 / 2010
Annales Polonici Mathematici 99 (2010), 45-53
MSC: Primary 47B35; Secondary 32A36.
DOI: 10.4064/ap99-1-4
Abstract
We prove a sufficient condition for products of Toeplitz operators $T_fT_{\bar g}$, where $f,g$ are square integrable holomorphic functions in the unit ball in $\mathbb C^n$, to be bounded on the weighted Bergman space. This condition slightly improves the result obtained by K. Stroethoff and D. Zheng. The analogous condition for boundedness of products of Hankel operators $H_fH^*_g$ is also given.
