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Article . 2025 . Peer-reviewed
Data sources: HELDA - Digital Repository of the University of Helsinki
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Article . 2025 . Peer-reviewed
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Lp→Lq boundedness of Fourier multipliers

descriptionPublicationkeyboard_double_arrow_right Article 19 Aug 2025 Finland English Publisher:Springer
Authors: Nursultanov M.;

handle: 10138/599998

Lp→Lq boundedness of Fourier multipliers

Abstract

This paper explores the boundedness of Fourier multipliers from Lp to Lq. We present new results that improve upon classical theorems due to Hörmander, Lizorkin, and Marcinkiewicz. In addition, we provide necessary conditions for the boundedness of Fourier multipliers. We introduce the concept of M-generalized monotone functions and sequences and derive criteria for the boundedness of Fourier multipliers corresponding to them.

Peer reviewed

Country
Finland
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Keywords

Hörmander’s theorem, Fourier multiplier, Fourier coefficient, Fourier transform, Lizorkin’s theorem, Marcinkiewicz’s theorem, Mathematics

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citations
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BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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impulse
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