A note on the Schrödinger maximal function

@article{Bourgain2016ANO,
  title={A note on the Schr{\"o}dinger maximal function},
  author={Jean Bourgain},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2016},
  volume={130},
  pages={393-396}
}
  • J. Bourgain
  • Published 19 September 2016
  • Mathematics
  • Journal d'Analyse Mathématique
It is shown that control of the Schrödinger maximal function sup0 <t<1 ǀeitΔfǀ for f ∈ Hs(Rn) requires s ≥ n/2(n + 1). 
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TLDR
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AbstractNew estimates on the maximal function associated to the linear Schrödinger equation are established. It is shown that the almost everywhere convergence property of eitΔf for t → 0 holds for f…
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A complete discretization scheme for an ill-posed Cauchy problem for abstract firstorder linear differential equations with sectorial operators in a Banach space is validated. The scheme combines a…
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A note on the almost everywhere behavior of solutions to the Schrödinger equation
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