Journal d'Analyse Mathématique

, Volume 130, Issue 1, pp 393–396 | Cite as

A note on the Schrödinger maximal function

Article

Abstract

It is shown that control of the Schrödinger maximal function sup0 <t<1 ǀeitΔfǀ for fHs(Rn) requires sn/2(n + 1).

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References

  1. [B]
    J. Bourgain, On the Schrödinger maximal function in higher dimension, Tr. Mat. Inst. Steklova 280 (2013), 53–66; reprinted in Proc. Steklov Inst. Math. 280 (2013), 46–60.MathSciNetCrossRefMATHGoogle Scholar
  2. [C]
    L. Carleson, Some analytic problems related to statistical mechanics, Euclidean Harmonic Analysis, Springer, Berlin, 1980, pp. 5–45.MATHGoogle Scholar
  3. [D-G]
    C. Demeter and S. Guo, Schrödinger maximal function estimates via the pseudoconformal transformation, arXiv:1608.07640[math.CA].Google Scholar
  4. [D-K]
    B. E. J. Dahlberg and C. E. Kenig, A note on the almost everywhere behavior of solutions to the Schrödinger equation, Harmonic Analysis, Springer, Berlin, 1982, pp. 205–209.MATHGoogle Scholar
  5. [L]
    S. Lee, On pointwise convergence of the solutions to Schrödinger equations in R2, Int. Math. Res. Not. 2006, Art ID 32597.Google Scholar
  6. [L-R]
    R. Lucà and K. Rogers, An improved necessary condition for the Schrödinger maximal estimate, arXiv1506.05325[math.CA].Google Scholar

Copyright information

© Hebrew University Magnes Press 2016

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA

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