Quasihomogeneous Toeplitz operators with integrable symbols on the harmonic Bergman space
Keywords:
Toeplitz operators, harmonic Bergman space, quasihomogeneous symbolsAbstract
In this paper, we completely determine the commutativity of two Toeplitz operators on the harmonic Bergman space with integrable quasihomogeneous symbols, one of which is of the form \(e^{ik\theta}r^m\). As an application, the problem that when their product is again a Toeplitz operator is solved. In particular, Toeplitz operators with bounded symbols on the harmonic Bergman space commute with \(T_{e^{ik\theta}r^m}\) only in trivial cases, which appears quite different from results of analytic Bergman spaces in Cuckovic and Rao, [Mellin transform, monomial symbols, and commuting Toeplitz operators, J. Funct. Anal. \(154\) (1998), 195--214.] DOI:- 10.1017/S0004972714000379Published
2014-09-20
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