  The bilinear estimtate in proposition 7.15 [J. Bourgain, Fourier restriction
phenomena for certain lattice subsets and applications to nonlinear evolution
equations, Parts II, Geometric Funct. Anal. 3(3) (1993) 209-262.] plays an
essential role in the study of the nonlinear term of KdV equation. In this
paper, this estimate is extended to the a more general water-vave equations. We
hope this result could shed some light on the estimates of nonlinear terms of
water-vave equations.
