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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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