On local smoothing problems and Stein's maximal 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.

16pages, 1figure

Cited by in corpus (2)

• Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
• The Spherical Maximal Operators on Hyperbolic Spaces