Structural resolvent estimates and derivative nonlinear Schrodinger   equations
  A refinement of uniform resolvent estimate is given and several smoothing estimates for Schrodinger equations in the critical case are induced from it. The relation between this resolvent estimate and radiation condition is discussed. As an application of critical smoothing estimates, we show a global existence results for derivative nonlinear Schrodinger equations. 
Michael Ruzhansky, Mitsuru Sugimoto
math.AP math.FA