Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations
| dc.creator | Tao, Terence | |
| dc.date | 2000-04-29 | |
| dc.date | 2004-03-04 | |
| dc.date.accessioned | 2026-07-07T04:34:55Z | |
| dc.date.available | 2026-07-07T04:34:55Z | |
| dc.description | The $X^{s,b}$ 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.description | 50 pages. An incorrect estimate has been fixed | |
| dc.identifier | https://arxiv.org/abs/math/0005001 | |
| dc.identifier | http://arxiv.org/abs/math/0005001 | |
| dc.identifier | Amer. J. Math. 123 (2001), 839-908 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59094 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35G25; 42B35 35L70, 35Q53, 35Q55 | |
| dc.title | Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations | |
| dc.type | text |