Global maximal estimates for solutions to the Schrödinger equation

Per Sjölin

Studia Mathematica (1994)

  • Volume: 110, Issue: 2, page 105-114
  • ISSN: 0039-3223

Abstract

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

How to cite

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Sjölin, Per. "Global maximal estimates for solutions to the Schrödinger equation." Studia Mathematica 110.2 (1994): 105-114. <http://eudml.org/doc/216103>.

@article{Sjölin1994,
abstract = {Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.},
author = {Sjölin, Per},
journal = {Studia Mathematica},
keywords = {Schrödinger equation; maximal estimates; Sobolev space; maximal functions},
language = {eng},
number = {2},
pages = {105-114},
title = {Global maximal estimates for solutions to the Schrödinger equation},
url = {http://eudml.org/doc/216103},
volume = {110},
year = {1994},
}

TY - JOUR
AU - Sjölin, Per
TI - Global maximal estimates for solutions to the Schrödinger equation
JO - Studia Mathematica
PY - 1994
VL - 110
IS - 2
SP - 105
EP - 114
AB - Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
LA - eng
KW - Schrödinger equation; maximal estimates; Sobolev space; maximal functions
UR - http://eudml.org/doc/216103
ER -

References

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  1. [1] J. Bourgain, A remark on Schrödinger operators, Israel J. Math., to appear. Zbl0798.35131
  2. [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. [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. [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. [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. [6] C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69. Zbl0738.35022
  7. [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. Zbl0737.35102
  8. [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. Zbl0525.42011
  9. [9] E. Prestini, Radial functions and regularity of solutions to the Schrödinger equation, Monatsh. Math. 109 (1990), 135-143. Zbl0777.42005
  10. [10] P. Sjölin, Convolution with oscillating kernels, Indiana Univ. Math. J. 30 (1981), 47-55. Zbl0419.47020
  11. [11] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715. Zbl0631.42010
  12. [12] P. Sjölin, Radial functions and maximal estimates for solutions to the Schrödinger equation, J. Austral. Math. Soc., to appear. Zbl0856.42013
  13. [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. [14] L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874-878. Zbl0654.42014

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