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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35J10, 35B45

Retrieve articles in all journals with MSC: 35J10, 35B45

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society