Duke Mathematical Journal

Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations

S. J. Montgomery-Smith

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J., Volume 91, Number 2 (1998), 393-408.

First available in Project Euclid: 19 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 35K10: Second-order parabolic equations 35L05: Wave equation


Montgomery-Smith, S. J. Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations. Duke Math. J. 91 (1998), no. 2, 393--408. doi:10.1215/S0012-7094-98-09117-7. https://projecteuclid.org/euclid.dmj/1077232084

Export citation


  • [Br] P. Brenner, On $L\sbp-L\sbp\sp\prime $ estimates for the wave-equation, Math. Z. 145 (1975), no. 3, 251–254.
  • [Co] R. R. Coifman, G. David, and Y. Meyer, La solution des conjecture de Calderón, Adv. in Math. 48 (1983), no. 2, 144–148.
  • [Gi] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear Schrödinger equations, J. Math. Pures Appl. (9) 64 (1985), no. 4, 363–401.
  • [Ha] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952.
  • [Ka] L. Kapitanski, Global and unique weak solutions of nonlinear wave equations, Math. Res. Lett. 1 (1994), no. 2, 211–223.
  • [Ke] C. E. Kenig, G. Ponce, and L. Vega, On the IVP for the nonlinear Schrödinger equations, Harmonic analysis and operator theory (Caracas, 1994), Contemp. Math., vol. 189, Amer. Math. Soc., Providence, RI, 1995, pp. 353–367.
  • [Kl] S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), no. 9, 1221–1268.
  • [Pe] K. E. Petersen, Brownian motion, Hardy spaces and bounded mean oscillation, Lecture Note Series, vol. 28, Cambridge University Press, Cambridge, 1977.
  • [Ru] A. Ruiz and L. Vega, Local regularity of solutions to wave equations with time-dependent potentials, Duke Math. J. 76 (1994), no. 3, 913–940.
  • [Se] E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993.
  • [St1] R. S. Strichartz, A priori estimates for the wave equation and some applications, J. Functional Analysis 5 (1970), 218–235.
  • [St2] R. S. Strichartz, Bounded mean oscillation and Sobolev spaces, Indiana Univ. Math. J. 29 (1980), no. 4, 539–558.