On Multilinear Fourier Multipliers of Limited Smoothness

Grafakos, Loukas ; Miyachi, Akihiko ; Tomita, Naohito

Canadian journal of mathematics, Tome 65 (2013) no. 2, pp. 299-330

Résumé

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.

Détail

DOI : 10.4153/CJM-2012-025-9

Mots-clés : 42B15, 42B20, multilinear Fourier multipliers, Hörmander multiplier theorem, Hardy spaces

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