On $L^p$-Estimates for the Time Dependent Schr?dinger Operator on $L^2$

摘要

Let denote the time-dependent Schr?dinger operator in space variables. We consider a variety of Lebesgue norms for functions on , and prove or disprove estimates for such norms of in terms of the norms of and . The results have implications for self-adjointness of operators of the form where is a multiplication operator. The proofs are based mainly on Strichartz-type inequalities.