Abstract

The Xs,b 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 L2 norms of the component functions. In this paper we systematically study weighted convolution estimates on L2. As a consequence we obtain sharp bilinear estimates for the KdV, wave, and Schrödinger Xs,b spaces.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 839-908
Launched on MUSE
2001-10-01
Open Access
No
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