Skip to main content

A note on the Schrödinger maximal function


It is shown that control of the Schrödinger maximal function sup0 <t<1 ǀe itΔ fǀ for fH s(Rn) requires sn/2(n + 1).

This is a preview of subscription content, access via your institution.


  1. 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.

    MathSciNet  Article  MATH  Google Scholar 

  2. L. Carleson, Some analytic problems related to statistical mechanics, Euclidean Harmonic Analysis, Springer, Berlin, 1980, pp. 5–45.

    MATH  Google Scholar 

  3. C. Demeter and S. Guo, Schrödinger maximal function estimates via the pseudoconformal transformation, arXiv:1608.07640[math.CA].

  4. 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.

    MATH  Google Scholar 

  5. S. Lee, On pointwise convergence of the solutions to Schrödinger equations in R2, Int. Math. Res. Not. 2006, Art ID 32597.

    Google Scholar 

  6. R. Lucà and K. Rogers, An improved necessary condition for the Schrödinger maximal estimate, arXiv1506.05325[math.CA].

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to J. Bourgain.

Additional information

The author was partially supported by NSF grants DMS-1301619.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bourgain, J. A note on the Schrödinger maximal function. JAMA 130, 393–396 (2016).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: