Open Access
2014 Boundedness criterion for bilinear Fourier multiplier operators
Akihiko Miyachi, Naohito Tomita
Tohoku Math. J. (2) 66(1): 55-76 (2014). DOI: 10.2748/tmj/1396875662

Abstract

Bilinear Fourier multiplier operators corresponding to multipliers that are singular at the origin are considered. New criterions on such multipliers to assure the boundedness of the corresponding operators from $L^p \times L^q$ to $L^r$, $1/p+1/q=1/r$, are given in the range $1<p,q \le \infty$, $2/3<r<\infty$.

Citation

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Akihiko Miyachi. Naohito Tomita. "Boundedness criterion for bilinear Fourier multiplier operators." Tohoku Math. J. (2) 66 (1) 55 - 76, 2014. https://doi.org/10.2748/tmj/1396875662

Information

Published: 2014
First available in Project Euclid: 7 April 2014

zbMATH: 1290.42029
MathSciNet: MR3189479
Digital Object Identifier: 10.2748/tmj/1396875662

Subjects:
Primary: 42B15
Secondary: 42B20

Keywords: bilinear Fourier multipliers , Hörmander multiplier theorem , Littlewood-Paley theory

Rights: Copyright © 2014 Tohoku University

Vol.66 • No. 1 • 2014
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