Multilinear weighted convolution of L2 functions, and applications to nonlinear dispersive equations

  title={Multilinear weighted convolution of L2 functions, and applications to nonlinear dispersive equations},
  author={Terence Tao},
  journal={American Journal of Mathematics},
  pages={839 - 908}
  • T. Tao
  • Published 29 April 2000
  • Mathematics
  • American Journal of Mathematics
<abstract abstract-type="TeX"><p>The <i>X<sup>s,b</sup></i> spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behavior of nonlinear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in terms of the <i>L</i><sup>2</sup> norms of the… 
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