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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the weighted estimate of the solution associated with the Schrödinger equation


Author: Si Lei Wang
Journal: Proc. Amer. Math. Soc. 113 (1991), 87-92
MSC: Primary 35J10; Secondary 35B45
MathSciNet review: 1069695
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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\vert {u(x,t)} \right\vert}^2}d... ...a}}dx \leq C{{\left\Vert f \right\Vert}_{{H^{ - 1 + a/2}}({\mathbb{R}^n})}}} } $ is false. Another improved weighted inequality is proved for the general case.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1069695-0
PII: S 0002-9939(1991)1069695-0
Article copyright: © Copyright 1991 American Mathematical Society