Pointwise convergence of the solutions to wave equations with potentials

Wang, Chengbo; Zhao, Shuijiang

doi:10.1090/proc/16380

Pointwise convergence of the solutions to wave equations with potentials
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by Chengbo Wang and Shuijiang Zhao;

Proc. Amer. Math. Soc. 151 (2023), 3817-3825

DOI: https://doi.org/10.1090/proc/16380

Published electronically: May 19, 2023

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Abstract:

We study the pointwise convergence of solutions to linear wave equations with potentials. Under some general assumptions about the potentials, we determine the sufficient and necessary condition for initial data in Sobolev spaces. Using the harmonic analysis on semigroups developed by Cowling, we prove positive results. One of the novelties is that we give a counterexample for the discrete maximal estimate instead of the usual continuous maximal estimate, which enables us to apply the Stein maximal principle to prove negative results.

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