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