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arXiv · 0802.3921

The commutants of certain Toeplitz operators on weighted Bergman spaces

Trieu Le
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Abstract

For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function $f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This paper describes all the functions $f$ for which $T_f$ commutes with a given $T_g$, where $g(z)=z_{1}^{L_1}... z_{n}^{L_n}$ for strictly positive integers $L_1,..., L_n$, or $g(z)=|z_1|^{s_1}... |z_n|^{s_n}h(|z|)$ for non-negative real numbers $s_1,..., s_n$ and a bounded measurable function $h$ on $[0,1)$.

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Trieu Le. 2008-02-26. The commutants of certain Toeplitz operators on weighted Bergman spaces. https://doi.org/10.1016/j.jmaa.2008.07.005

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