2018/03/01 by Cao Jiang, Jiang, Cao, Xing-Tang Dong +3
Mathematics · #32A36 #47B35 #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1803.00237
openalex publication_date 2018/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.