• Corpus ID: 232404792

Counterexamples for high-degree generalizations of the Schr\"odinger maximal operator

  title={Counterexamples for high-degree generalizations of the Schr\"odinger maximal operator},
  author={Chen An and Rena Chu and L. B. Pierce},
. In 1980 Carleson posed a question on the minimal regularity of an initial data function in a Sobolev space H s ( R n ) that implies pointwise convergence for the solution of the linear Schr¨odinger equation. After progress by many authors, this was recently resolved (up to the endpoint) by Bourgain, whose counterexample construction for the Schr¨odinger maximal operator proved a necessary condition on the regularity, and Du and Zhang, who proved a sufficient condition. Analogues of Carleson’s… 
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