  We develop inverse scattering for the derivative nonlinear Schrodinger
equation (DNLS) on the line using its gauge equivalence with a related
nonlinear dispersive equation. We prove Lipschitz continuity of the direct and
inverse scattering maps from the weighted Sobolev spaces $H^{2,2}(\mathbb{R})$
to itself. These results immediately imply global existence of solutions to the
DNLS for initial data in a spectrally determined (open) subset of
$H^{2,2}(\mathbb{R})$ containing a neighborhood of 0.
