Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 55, pp. 1-7.

Title: A note on local smoothing effects for the
       unitary group associated with the KdV equation
 
Author: Xavier Carvajal (Instituto de Mat. - UFRJ, Brazil)

Abstract: 
 In this note we show interesting local smoothing effects for the
 unitary group associated to Korteweg-de Vries type equation.
 Our main tools are the Hardy-Littlewood-Sobolev and Hausdorff-Young 
 inequalities.  Using our local smoothing effect and a dual version, 
 we estimate the growth of the norm of solutions of the
 complex modified KdV equation.
 
Submitted March 13, 2008. Published April 17, 2008.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Modified KdV equation; KdV equation; local smoothing effect.