Global smoothing properties of generalized Schrödinger equations (Q1283058)

The author proves regularity results of type `decay implies smoothing' for the free homogeneous and inhomegeneous time-dependent Schrödinger equation, for more general equations of similar type, and also for linear problems of wave equation type. The results are generalizations of earlier ones of the same type by Constantin and Saut, Kato and Yajima, Kenig, Ponce and Vega, and others. The proofs crucially use refined resolvent estimates (proved by the author and T. Tsujimoto) for the linear differential operator involved in the equations, weighted Hardy spaces, and restriction type theorems.