JournalsrmiVol. 29, No. 2pp. 495–530

Minimal smoothness conditions for bilinear Fourier multipliers

  • Akihiko Miyachi

    Tokyo Woman's Christian University, Japan
  • Naohito Tomita

    Osaka University, Japan
Minimal smoothness conditions  for bilinear Fourier multipliers cover
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Abstract

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 Hp1×Hp2H^{p_1}\times H^{p_2} to LpL^p, 1/p1+1/p2=1/p1/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<p1,p20 < p_1, p_2 \leq \infty.

Cite this article

Akihiko Miyachi, Naohito Tomita, Minimal smoothness conditions for bilinear Fourier multipliers. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 495–530

DOI 10.4171/RMI/728