On the weighted estimate of the solution associated with the Schrödinger equation
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- by Si Lei Wang
- Proc. Amer. Math. Soc. 113 (1991), 87-92
- DOI: https://doi.org/10.1090/S0002-9939-1991-1069695-0
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Abstract:
Let $u(x,t)$ be the solution of the Schrödinger equation with initial data $f$ in the Sobolev space ${H^{ - 1 + a/2}}({\mathbb {R}^n})$ with $a > 1$. This paper shows that the weighted inequality $\int _{{\mathbb {R}^n}} {\int _\mathbb {R} {{{\left | {u(x,t)} \right |}^2}dt{{(1 + \left | x \right |)}^{ - a}}dx \leq C{{\left \| f \right \|}_{{H^{ - 1 + a/2}}({\mathbb {R}^n})}}} }$ is false. Another improved weighted inequality is proved for the general case.References
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Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 87-92
- MSC: Primary 35J10; Secondary 35B45
- DOI: https://doi.org/10.1090/S0002-9939-1991-1069695-0
- MathSciNet review: 1069695