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On Multilinear Fourier Multipliers of Limited Smoothness

Published online by Cambridge University Press:  20 November 2018

Loukas Grafakos ,
Akihiko Miyachi  and
Naohito Tomita
Loukas Grafakos
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA, e-mail: grafakosl@missouri.edu
Akihiko Miyachi
Affiliation:
Department of Mathematics, Tokyo Woman's Christian University, Zempukuji, Suginami-ku, Tokyo 167- 8585, Japan, e-mail: miyachi@lab.twcu.ac.jp
Naohito Tomita
Affiliation:
Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan, e-mail: tomita@math.sci.osaka-u.ac.jp
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Abstract

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In this paper we prove a certain ${{L}^{2}}$-estimate for multilinear Fourier multiplier operators with multipliers of limited smoothness. As a consequence, we extend the result of Calderón and Torchinsky in the linear theory to the multilinear case. The sharpness of our results and some related estimates in Hardy spaces are also discussed.

Keywords

42B1542B20multilinear Fourier multipliersHörmander multiplier theoremHardy spaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 2 , 01 April 2013 , pp. 299 - 330
Copyright
Copyright © Canadian Mathematical Society 2013

References

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