Regularizing estimates for Schrödinger and wave equations

Alberto Ruiz

Journées équations aux dérivées partielles (1993)

  • Volume: 1993, Issue: 5, page 1-12
  • ISSN: 0752-0360

How to cite


Ruiz, Alberto. "Regularizing estimates for Schrödinger and wave equations." Journées équations aux dérivées partielles 1993.5 (1993): 1-12. <>.

author = {Ruiz, Alberto},
journal = {Journées équations aux dérivées partielles},
keywords = {initial value problems; Morrey-Campanato class; weighted estimates},
language = {eng},
number = {5},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {Regularizing estimates for Schrödinger and wave equations},
url = {},
volume = {1993},
year = {1993},

AU - Ruiz, Alberto
TI - Regularizing estimates for Schrödinger and wave equations
JO - Journées équations aux dérivées partielles
PY - 1993
PB - Ecole polytechnique
VL - 1993
IS - 5
SP - 1
EP - 12
LA - eng
KW - initial value problems; Morrey-Campanato class; weighted estimates
UR -
ER -


  1. [AH] Agmon S., Hörmander L., Asymptotic properties of solutions of differential equations with simple characteristics. J. d'Analyse Mathématique, Vol. 30, 1976, 1-28 Zbl0335.35013MR57 #6776
  2. [ChR] Chiarenza F., Ruiz A., Uniform L2 weighted Sobolev inequalities. Proc. AMS., 112, (1), 1991, 53-64. Zbl0745.35007MR91h:46057
  3. [ChF] Chiarenza, Frasca, A remark on a paper by C. Fefferman. Proc AMS, 1990 Zbl0694.46029
  4. [CS1] Constantin P., Saut J.C., Local smoothing properties of dispersive equations. J. of the AMS, 1, 1988, 413-139. Zbl0667.35061MR89d:35150
  5. [CS2] Constantin P., Saut J.C., Local smoothing properties of Schrödinger equations. Indiana U. Math. J., 38, 3, 1989, 791-810. Zbl0712.35022MR91e:35167
  6. [FP] C. Fefferman, P.Phong, Lower bounds for Schrödinger equations. Journes Eqs. D. P. St. Jean de Monts 1982. Zbl0492.35057
  7. [H] Harmse, J.On Lebesgue space estimates for the wave equation. Indiana University Math Journal 39.1 1990 Zbl0683.35008MR91j:35158
  8. [LP] Lions P.L., Perthame B., Lemmes de moments, de moyenne et de dispersion. C.R. Acad. Sci. Paris, t 314, Série, p. 801-806. 1992. Zbl0761.35085MR93f:35217
  9. [K] Kato T.On the Cauchy problem for the (generalized) KdV equation. Adv. in Math. Supplementary Studies, Studies in Applied Math., 8, 1983, 93-128. Zbl0549.34001MR86f:35160
  10. [KY] Kato T., Yajima K., Some examples of smooth operators and the associated smoothing effect. Review in Math. Physics, 1, 4, 1989. Zbl0833.47005MR91i:47013
  11. [KPV2] Kenig C., Ponce G., Vega L., Small solutions for non linear Schrödinger equations. To appear in Ann. I. Henri Poincaré. Zbl0786.35121
  12. [KRS] Kenig C., Ruiz A., Sogge C., Uniform Sobolev inequalities and unique continuation for second order constant coefficients differential operators. Duke Math. J., 55, 1987, 329-347. Zbl0644.35012MR88d:35037
  13. [RV] Ruiz A., Vega L., Unique continuation for Schrödinger operators with potential in Morrey spaces. Publications Matemátiques, 35, 1991, 291-298. Zbl0809.47046MR92e:35039
  14. [RV2] Ruiz A., Vega L., On local regularity of Schrödinger equations. Int. Math. Research Notices. N 1. 13-27. Duke Math. J. 1993 Zbl0812.35016MR94c:35060
  15. [RV3] Smoothing effect for Schródinger and wave equations. In preparation 
  16. [SSj] Sjögren P., Sjölin P., Convergence properties for the time dependent Schrödinger equation. To appear in Ann. Acad. Sci. Fenn.. Zbl0629.35055
  17. [Sj] Sjölin P., Regularity of solutions to the Schrödinger equations. Duke Math. J., 55, 1987, 699-715. Zbl0631.42010
  18. [So] Soffer A., Phase space analysis of non linear waves and global existence. Preprint. 
  19. [T] Tomas P., A restriction theorem for the Fourier transform. Bull. AMS, 81, 1975, 477-478. Zbl0298.42011MR50 #10681
  20. [V1] Vega L., Schrödinger equations : pointwise convergence to the initial data. Proc. AMS, 102, 1988, 874-878. Zbl0654.42014MR89d:35046
  21. [V2] Vega L., El multiplicador de Schrödinger : la función maximal y los operadores de restricción. Tesis doctoral. Universidad Autónoma de Madrid. 1988. 
  22. [Y] Yajima K., Existence of solutions for Schrödinger Evolution Equations. Comm. Math. Phys., 110 (1987), 415-426. Zbl0638.35036MR88e:35048

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