New York Journal of Mathematics
Volume 21 (2015) 1327-1345


Akaki Tikaradze

Multiplication operators on the Bergman spaces of pseudoconvex domains

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Published: December 16, 2015
Keywords: Bergman spaces, pseudoconvex domains, multiplication operators
Subject: Primary 32A36; Secondary 47B35

Let Ω⊂ Cn be a bounded smooth pseudoconvex domain, and let f=(f1,..., fn):\overline{Ω}⊂Cn be an n-tuple of holomorphic functions on \overline{Ω}. In this paper we study commutants of the corresponding multiplication operators {Tf1, ..., Tfn}=Tf on the Bergman space A2(Ω). One of our main results is a geometric description of the algebra of commutants of {Tf, Tf*}, generalizing a result by Douglas, Sun and Zheng, 2011.

Author information

University of Toledo, Department of Mathematics & Statistics, Toledo, OH 43606, USA