On local smoothing problems and Stein's maximal spherical means

TL;DR

This paper demonstrates that resolving the local smoothing conjecture for wave equations could lead to significant advancements in Stein's maximal spherical means, linking two important areas in harmonic analysis.

Contribution

It establishes a connection between the local smoothing conjecture and Stein's maximal spherical means, suggesting that progress in one could benefit the other.

Findings

Local smoothing conjecture implies improvements on Stein's maximal spherical means

Discussion of related problems in harmonic analysis

Potential implications for wave equations and spherical means

Abstract

It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are also discussed.