Multilinear weighted convolution of L-2 functions, and applications to nonlinear dispersive equations

The X-s,X-b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerma n-Machedon and others, are fundamental tools to study the low-regularity be havior of nonlinear dispersive equations. It is of particular interest to o btain bilinear or multilinear estimates involving these spaces. By Plancher el's theorem and duality, these estimates reduce to estimating a weighted c onvolution integral in terms of the L-2 norms of the component functions. I n this paper we systematically study weighted convolution estimates on L-2. As a consequence we obtain sharp bilinear estimates for the KdV, wave, and Schrodinger X-s,X-b spaces.