# Global maximal estimates for solutions to the Schrödinger equation

Studia Mathematica (1994)

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

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topSjölin, 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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- [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.
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- [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. Zbl0738.35022
- [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] 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] E. Prestini, Radial functions and regularity of solutions to the Schrödinger equation, Monatsh. Math. 109 (1990), 135-143. Zbl0777.42005
- [10] P. Sjölin, Convolution with oscillating kernels, Indiana Univ. Math. J. 30 (1981), 47-55. Zbl0419.47020
- [11] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715. Zbl0631.42010
- [12] P. Sjölin, Radial functions and maximal estimates for solutions to the Schrödinger equation, J. Austral. Math. Soc., to appear. Zbl0856.42013
- [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. Zbl0654.42014

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