(L_p\rightarrow L_q\) boundedness of Fourier multipliers

We investigate the \(L_p \mapsto L_q\) boundedness of the Fourier multipliers. We obtain sufficient conditions, namely, we derive Hormander and Lizorkin type theorems. We also obtain the necessary conditions. For \(M\)-generalized monotone functions, we obtain a criteria for boundedness of the corre...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Author: Nursultanov, Medet
Format: Article
Language:English
Subjects:
Monotone functions
Multipliers
Online Access:Get full text
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Summary:We investigate the \(L_p \mapsto L_q\) boundedness of the Fourier multipliers. We obtain sufficient conditions, namely, we derive Hormander and Lizorkin type theorems. We also obtain the necessary conditions. For \(M\)-generalized monotone functions, we obtain a criteria for boundedness of the corresponding Fourier multipliers.
ISSN:2331-8422