Abstract
We prove that two Toeplitz operators acting on the pluriharmonic Bergman space with radial symbol and pluriharmonic symbol respectively commute only in an obvious case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Brown and P. R. Halmos: Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213 (1963/64), 89-102.
B. R. Choe and Y. J. Lee: Commuting Toeplitz operators on the harmonic Bergman space. Michigan Math. J. 46 (1999), 163-174.
B. R. Choe and Y. J. Lee: Pluriharmonic symbols of commuting Toeplitz operators. Illinois J. Math. 37 (1993), 424-436.
Ž. Čučković and N. V. Rao: Mellin transform, monomial symbols, and commuting Toeplitz operators. J. Funct. Anal. 154 (1998), 195-214.
Y. J. Lee: Pluriharmonic symbols of commuting Toeplitz type operators. Bull. Austral. Math. Soc. 54 (1996), 67-77.
Y. J. Lee: Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces. Canad. Math. Bull. 41 (1998), 129-136.
Y. J. Lee and K. Zhu: Some differential and integral equations with applications to Toeplitz operators. Integral Equation Operator Theory 44 (2002), 466-479.
S. Ohno: Toeplitz and Hankel operators on harmonic Bergman spaces. Preprint.
W. Rudin: Function Theory in the Unit Ball of ℂn. Springer-Verlag, Berlin-Heidelberg-New York, 1980.
D. Zheng: Commuting Toeplitz operators with pluriharmonic symbols. Trans. Amer. Math. Soc. 350 (1998), 1595-1618.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lee, Y.J. Commuting Toeplitz Operators on the Pluriharmonic Bergman Space. Czechoslovak Mathematical Journal 54, 535–544 (2004). https://doi.org/10.1023/B:CMAJ.0000042589.81321.4c
Issue Date:
DOI: https://doi.org/10.1023/B:CMAJ.0000042589.81321.4c