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  Volume 8, Issue 3, Article 80
 
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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