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Abstract <p> We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of the Fourier transform. We characterize analytic functions in these spaces and, in particular, give an analog of the Paley–Wiener theorem in this setting. As an application, we consider Toeplitz operators with vertical symbols in these new spaces. </p>

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Mixed Fourier Norm Spaces of Analytic Functions on the Upper Half-Plane and Toeplitz Operators

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Z. G. Avetisyan,
  • A. N. Karapetyants,
  • I. Smirnova

摘要

Abstract

We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of the Fourier transform. We characterize analytic functions in these spaces and, in particular, give an analog of the Paley–Wiener theorem in this setting. As an application, we consider Toeplitz operators with vertical symbols in these new spaces.