Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations

dc.creatorTao, Terence
dc.date2000-04-29
dc.date2004-03-04
dc.date.accessioned2026-07-07T04:34:55Z
dc.date.available2026-07-07T04:34:55Z
dc.descriptionThe $X^{s,b}$ spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear 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 $L^2$ norms of the component functions. In this paper we systematically study weighted convolution estimates on $L^2$. As a consequence we obtain sharp bilinear estimates for the KdV, wave, and Schrödinger $X^{s,b}$ spaces.
dc.description50 pages. An incorrect estimate has been fixed
dc.identifierhttps://arxiv.org/abs/math/0005001
dc.identifierhttp://arxiv.org/abs/math/0005001
dc.identifierAmer. J. Math. 123 (2001), 839-908
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59094
dc.subjectAnalysis of PDEs
dc.subject35G25; 42B35 35L70, 35Q53, 35Q55
dc.titleMultilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations
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