This article is cited in 3 papers

Papers published in the English version of the journal

Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators

Z. G. Avetisyan^a, A. N. Karapetyants^b, I. Smirnova<sup>c

a</sup> Ghent University, Belgium
^b Institute of Mathematics, Mechanics and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don
^c Don State Technical University, Rostov-on-Don

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.

Keywords: mixed norm space, analytic function, Paley–Wiener theorem, Toeplitz operator.

Received: 14.01.2025
Revised: 14.01.2025

Language: English

 English version: Mathematical Notes, 2025, 117:3, 345–356

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