The Berezin transform and Toeplitz operators on the Bergman space over the quarter plane

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Hocine Guediri

Abstract

In this note, we introduce Bergman spaces on the complex upper-right quarter-plane (the first quadrant), and establish some of their fundamental properties. Moreover, we study the associated Berezin transform, and we deduce characterizations of bounded as well as compact Toeplitz operators with symbols that are either harmonic or continuous.

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How to Cite
Guediri, H. (2024). The Berezin transform and Toeplitz operators on the Bergman space over the quarter plane. Gulf Journal of Mathematics, 16(2), 12-26. https://doi.org/10.56947/gjom.v16i2.1841
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