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On Multilinear Fourier Multipliers of Limited Smoothness

Published:2012-08-27
Printed: Apr 2013
• Loukas Grafakos,
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
• Akihiko Miyachi,
Department of Mathematics, Tokyo Woman's Christian University, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
• Naohito Tomita,
Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
 Format: LaTeX MathJax PDF

Abstract

In this paper, we prove certain $L^2$-estimate for multilinear Fourier multiplier operators with multipliers of limited smoothness. As a result, 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: multilinear Fourier multipliers, Hörmander multiplier theorem, Hardy spaces
 MSC Classifications: 42B15 - Multipliers 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)

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