Action of a scattering map on weighted Sobolev spaces in the plane

Abstract

We consider a scattering map that arises in the $\bar{\partial }$-approach to the scattering theory for the Davey-Stewartson II equation and show that the map is an invertible map between certain weighted $L^2$ Sobolev spaces.

The appendix is by R.M. Brown and N. Serpico. Version 2--minor corrections

References in corpus (3)

• Estimates for a family of multi-linear forms
• Global Well-Posedness and Long-time Asymptotics for the Defocussing Davey-Stewartson II Equation in $H^{1,1}(R^2)$
• A Sharp analog of Young's Inequality on $S^N$ and Related Entropy Inequalities