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On the powers of quasihomogeneous Toeplitz operators

Aissa Bouhali; Zohra Bendaoud; Issam Louhichi — 2021

Czechoslovak Mathematical Journal

We present sufficient conditions for the existence of $p$ th powers of a quasihomogeneous Toeplitz operator $T_{e^{i s θ} ψ}$ , where $ψ$ is a radial polynomial function and $p$ , $s$ are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.

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