JIPAM

On $L^p$-Estimates for the Time Dependent Schrödinger Operator on $L^2$  
 
  Authors: Mohammed Hichem Mortad,  
  Keywords: Schrödinger Equation, Strichartz Estimates and Self-adjointness.  
  Date Received: 07/07/07  
  Date Accepted: 29/08/07  
  Subject Codes:

Pri: 35B45; Sec: 35L10.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

Let $ L$ denote the time-dependent Schrödinger operator in $ n$ space variables. We consider a variety of Lebesgue norms for functions $ u$ on $ {mathbb{R}^{n+1}}$, and prove or disprove estimates for such norms of $ u$ in terms of the $ L^2$ norms of $ u$ and $ Lu$. The results have implications for self-adjointness of operators of the form $ L+V$ where $ V$ is a multiplication operator. The proofs are based mainly on Strichartz-type inequalities. ;


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