In this paper, we consider the trace theorem for modulation spaces, alpha modulation spaces and Besov spaces. For the modulation space, we obtain the sharp results.
We study the Cauchy problem for the generalized elliptic and non-elliptic derivative nonlinear Schrodinger equations, the existence of the scattering operators and the global well posedness of solutions with small data in Besov spaces and in modulati
on spaces are obtained. In one spatial dimension, we get the sharp well posedness result with small data in critical homogeneous Besov spaces. As a by-product, the existence of the scattering operators with small data is also shown. In order to show these results, the glob
