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Abstract <p> On the upper half-plane, we introduce weighed mixed norm function spaces defined in terms of the Mellin transform. We describe the corresponding space of analytic functions and characterize the analytic functions in this space. In particular, we give an analog of the Paley–Wiener theorem. As an application, in these spaces of analytic functions we consider Toeplitz operators with symbols depending on the angular variable. </p>

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Weighted Spaces of Analytic Functions on the Upper Half-Plane with Mixed Norm Defined in Terms of the Mellin Transform and Toeplitz Operators

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • I. Yu. Smirnova

摘要

Abstract

On the upper half-plane, we introduce weighed mixed norm function spaces defined in terms of the Mellin transform. We describe the corresponding space of analytic functions and characterize the analytic functions in this space. In particular, we give an analog of the Paley–Wiener theorem. As an application, in these spaces of analytic functions we consider Toeplitz operators with symbols depending on the angular variable.