Integrability of the Fourier transform via Riesz derivative

Elijah Liflyand; Stefan Samko

doi:10.1017/s0017089526100937

Integrability of the Fourier transform via Riesz derivative

Elijah Liflyand
, Stefan Samko

Department of Mathematics

University of Algarve

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Glasgow Mathematical Journal
DOIs	https://doi.org/10.1017/s0017089526100937
State	Accepted/In press - 2026

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© The Author(s), 2026. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust.

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title = "Integrability of the Fourier transform via Riesz derivative",

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.",

author = "Elijah Liflyand and Stefan Samko",

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AU - Samko, Stefan

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AB - 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.

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JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

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Integrability of the Fourier transform via Riesz derivative

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