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arXiv · 1912.10574

On Bourgain's counterexample for the Schr\"odinger maximal function

Lillian B. Pierce
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Abstract

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 Schr\"odinger 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.

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Lillian B. Pierce. 2019-12-23. On Bourgain's counterexample for the Schr\"odinger maximal function. https://arxiv.org/abs/1912.10574

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