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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
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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 multilinear Fourier multipliers, Hörmander multiplier theorem, Hardy spaces
MSC Classifications: 42B15, 42B20 show english descriptions Multipliers
Singular and oscillatory integrals (Calderon-Zygmund, etc.)
42B15 - Multipliers
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
 

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