Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1991-1069695-0
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?)

  • [AH] N. E. Aguilera and E. O. Harboure, Some inequalities for maximal operators, Indiana Univ. Math. J. 29 (1980), 559-576. MR 578206 (81k:42015)
  • [L] Y. L. Luke, Integrals of Bessel functions, McGraw-Hill, New York, 1962. MR 0141801 (25:5198)
  • [SW] E. M. Stein and G. Weiss, Introduction to Fourier analysis in Euclidean spaces, Princeton Univ. Press, Princeton, NJ, 1975. MR 1970295 (2004a:42001)
  • [V] L. Vega, Schrödinger equations: Pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874-878. MR 934859 (89d:35046)

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

DOI: https://doi.org/10.1090/S0002-9939-1991-1069695-0
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society