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Radial functions and maximal estimates for solutions to the Schrödinger equation

Published online by Cambridge University Press:  09 April 2009

Per Sjölin
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden, email: [email protected]
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Abstract

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Maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation. The initial value function is assumed to be radial in ℝn, n≥2.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bourgain, J., ‘A remark on Schrödinger operators’, Israel J. Math. 77 (1992), 116.CrossRefGoogle Scholar
[2]Carbery, A., ‘Radial Fourier multipliers and associated maximal functions’, in: Recent Progress in Fourier Analysis, North-Holland Mathematics Studies 111 (North-Holland, Amsterdam, 1985) pp. 4956.Google Scholar
[3]Carleson, L., ‘Some analytical problems related to statistical mechanics’, in: Euclidean Harmonic Analysis, Lecture Notes in Math. 779 (Springer, Berlin, 1979) pp. 545.Google Scholar
[4]Cowling, M., ‘Pointwise behaviour of solutions to Schrödinger equations’, in: Harmonic Analysis, Lecture Notes in Math. 992 (Springer, Berlin, 1983) pp. 8390.CrossRefGoogle Scholar
[5]Dahlberg, B. E. J. and Kenig, C. E., ‘A note on the almost everywhere behaviour of solutions to the Schödinger equation’, in: Harmonic Analysis, Lecture Notes in Math. 908 (Springer, Berlin, 1982) pp. 205209.CrossRefGoogle Scholar
[6]Kenig, C. E. and Ruiz, A., ‘A strong type (2,2) estimate for a maximal operator associated to the Schödinger equation’, Trans. Amer. Math Soc. 280 (1983), 239246.Google Scholar
[7]Kenig, C. E., Ponce, G. and Vega, L., ‘Oscillatory integrals and regularity of dispersive equations’, Indiana Univ. Math. J. 40 (1991), 3369.CrossRefGoogle Scholar
[8]Muckenhoupt, B., ‘Weighted norm inequalities for the Fourier transform’, Trans. Amer. Math. Soc. 276 (1983), 729742.CrossRefGoogle Scholar
[9]Prestini, E., ‘Radial functions and regularity of solutions to the Schödinger equation’, Monatsh. Math. 109 (1990), 135143.CrossRefGoogle Scholar
[10]Sjölin, P., ‘Regularity of solutions to the Schödinger equation’, Duke Math. J. 55 (1987), 699715.CrossRefGoogle Scholar
[11]Stein, E. M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Space (Princeton Univ. Press, Princeton, 1971).Google Scholar
[12]Vega, L., ‘Schödinger equtions: pointwise convergence to the initial data’, Proc. Amer. Math. Soc. 102 (1988), 874878.Google Scholar