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Integrability of the Fourier transform via Riesz derivative

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  29 May 2026

Elijah Liflyand Open the ORCID record for Elijah Liflyand [Opens in a new window]  and
Stefan Samko
Elijah Liflyand*
Affiliation:
Bar-Ilan University, Israel
Stefan Samko
Affiliation:
Departamento de Matemática, Universidade do Algarve, Portugal Kh. Ibragimov Complex Institute of Russian Academy of Sciences, Grozny, Russia
*
Corresponding author: Elijah Liflyand; Email: liflyand@gmail.com
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Abstract

A known condition for the integrability of the one-dimensional Fourier transform, in which the derivative is assumed to belong to the real Hardy space, is extended to the $n$-dimensional case, in terms of the $n$-th Riesz derivative. We obtain results for the Riesz derivatives of other orders. The function spaces involved in this study are compared and analyzed.

MSC classification

Primary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 42B35: Function spaces arising in harmonic analysis

Information

Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 8
Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

‡

This article has been updated since original publication. A notice detailing the change has been published.

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