ON BOURGAIN’S COUNTEREXAMPLE for the SCHRÖDINGER MAXIMAL FUNCTION

Journal Article (Journal Article)

This paper provides a rigorous derivation of a counterexample of Bourgain, related to a well-known question of pointwise a.e. convergence for the solution of the linear Schrödinger equation, for initial data in a Sobolev space. This counterexample combines ideas from analysis and number theory, and the present paper demonstrates how to build such counterexamples from first principles, and then optimize them.

Full Text

Duke Authors

Cited Authors

  • Pierce, LB

Published Date

  • December 1, 2020

Published In

Volume / Issue

  • 71 / 4

Start / End Page

  • 1309 - 1344

Electronic International Standard Serial Number (EISSN)

  • 1464-3847

International Standard Serial Number (ISSN)

  • 0033-5606

Digital Object Identifier (DOI)

  • 10.1093/qmath/haaa032

Citation Source

  • Scopus