The commutants of certain Toeplitz operators on weighted Bergman spaces

Abstract

For $\alpha >-1$, let $A_{\alpha }^2$ 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 $A_{\alpha }^2$. 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 $[0,1)$.

18 pages

Cited by in corpus (6)

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• Monomial-type Toeplitz operators on some weakly pseudoconvex domains
• Commutants of Toeplitz operators with radial symbols on the Fock-Sobolev space