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arXiv · 1803.00237

Monomial-type Toeplitz operators on some weakly pseudoconvex domains

Cao Jiang·Xing-Tang Dong·Ze-Hua Zhou
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Abstract

In this paper, we completely characterize the finite rank commutator and semi-commutator of two monomial-type Toeplitz operators on the Bergman space of certain weakly pseudoconvex domains. Somewhat surprisingly, there are not only plenty of commuting monomial-type Toeplitz operators but also non-trivial semi-commuting monomial-type Toeplitz operators. Our results are new even for the unit ball.%The situation is different from the case of unit disk. %Our results extend several known results using completely different arguments. Some interesting higher-dimensional phenomena appear on the unit polydisk.

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Cao Jiang, Xing-Tang Dong, Ze-Hua Zhou. 2018-03-01. Monomial-type Toeplitz operators on some weakly pseudoconvex domains. https://arxiv.org/abs/1803.00237

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