Revista Matemática Iberoamericana


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Volume 29, Issue 2, 2013, pp. 495–530
DOI: 10.4171/RMI/728

Published online: 2013-04-22

Minimal smoothness conditions for bilinear Fourier multipliers

Akihiko Miyachi[1] and Naohito Tomita[2]

(1) Tokyo Woman's Christian University, Japan
(2) Osaka University, Japan

The problem of finding the differentiability conditions for bilinear Fourier multipliers that are as small as possible to ensure the boundedness of the corresponding operators from products of Hardy spaces $H^{p_1}\times H^{p_2}$ to $L^p$, $1/p_1 +1/p_2 =1/p$, is considered. The minimal conditions in terms of the product type Sobolev norms are given for the whole range $0 < p_1, p_2 \leq \infty$.

Keywords: Bilinear Fourier multipliers, Hörmander multiplier theorem, Hardy spaces

Miyachi Akihiko, Tomita Naohito: Minimal smoothness conditions for bilinear Fourier multipliers. Rev. Mat. Iberoamericana 29 (2013), 495-530. doi: 10.4171/RMI/728