Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-16T05:49:16.064Z Has data issue: false hasContentIssue false
  • English
  • Français

Radial functions and maximal estimates for solutions to the Schrödinger equation

Part of: Harmonic analysis in several variables Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  09 April 2009

Per Sjölin
Per Sjölin
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden, email: pers@math.kth.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory 35Q40: PDEs in connection with quantum mechanics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 134 - 142
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bourgain, J., ‘A remark on Schrödinger operators’, Israel J. Math. 77 (1992), 1–16.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. 49–56.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. 5–45.Google Scholar
[4]Cowling, M., ‘Pointwise behaviour of solutions to Schrödinger equations’, in: Harmonic Analysis, Lecture Notes in Math. 992 (Springer, Berlin, 1983) pp. 83–90.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. 205–209.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), 239–246.Google Scholar
[7]Kenig, C. E., Ponce, G. and Vega, L., ‘Oscillatory integrals and regularity of dispersive equations’, Indiana Univ. Math. J. 40 (1991), 33–69.CrossRefGoogle Scholar
[8]Muckenhoupt, B., ‘Weighted norm inequalities for the Fourier transform’, Trans. Amer. Math. Soc. 276 (1983), 729–742.CrossRefGoogle Scholar
[9]Prestini, E., ‘Radial functions and regularity of solutions to the Schödinger equation’, Monatsh. Math. 109 (1990), 135–143.CrossRefGoogle Scholar
[10]Sjölin, P., ‘Regularity of solutions to the Schödinger equation’, Duke Math. J. 55 (1987), 699–715.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), 874–878.Google Scholar