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ArticleOriginal scientific text

Title

Global maximal estimates for solutions to the Schrödinger equation

Authors 1

Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Abstract

Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.

Bibliography

  1. J. Bourgain, A remark on Schrödinger operators, Israel J. Math., to appear.
  2. A. Carbery, Radial Fourier multipliers and associated maximal functions, in: Recent Progress in Fourier Analysis, Proc. Seminar on Fourier Analysis held in El Escorial, Spain, 1983, North-Holland Math. Stud. 111, North-Holland, 1985, 49-56.
  3. L. Carleson, Some analytical problems related to statistical mechanics, in: Euclidean Harmonic Analysis, Proc. Seminars held at the Univ. of Maryland, 1979, Lecture Notes in Math. 779, Springer, 1979, 5-45.
  4. M. Cowling, Pointwise behaviour of solutions to Schrödinger equations, in: Harmonic Analysis, Proc. Conf. Cortona, Italy, 1982, Lecture Notes in Math. 992, Springer, 1983, 83-90.
  5. B. E. J. Dahlberg and C. E. Kenig, A note on the almost everywhere behaviour of solutions to the Schrödinger equation, in: Harmonic Analysis, Proc. Conf. Univ. of Minnesota, Minneapolis, 1981, Lecture Notes in Math. 908, Springer, 1982, 205-209.
  6. C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69.
  7. C. E. Kenig, G. Ponce and L. Vega, Well-posedness of the initial value problem for the Korteweg-de Vries equation, J. Amer. Math. Soc. 4 (1991), 323-347.
  8. C. E. Kenig and A. Ruiz, A strong type (2,2) estimate for a maximal operator associated to the Schrödinger equation, Trans. Amer. Math. Soc. 280 (1983), 239-245.
  9. E. Prestini, Radial functions and regularity of solutions to the Schrödinger equation, Monatsh. Math. 109 (1990), 135-143.
  10. P. Sjölin, Convolution with oscillating kernels, Indiana Univ. Math. J. 30 (1981), 47-55.
  11. P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715.
  12. P. Sjölin, Radial functions and maximal estimates for solutions to the Schrödinger equation, J. Austral. Math. Soc., to appear.
  13. E. M. Stein, Oscillatory integrals in Fourier analysis, in: Beijing Lectures in Harmonic Analysis, Ann. of Math. Stud. 112, Princeton Univ. Press, 1986, 307-355.
  14. L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874-878.
Studia Mathematica
1994/110/2
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Pages:
105-114
Main language of publication
English
Received
1993-02-02
Published
1994
Exact and natural sciences