APDE seminar@BCAM: Maximal averages over hypersurfaces

Abstract

Stein's spherical maximal function can be generalized to maximal averages over general hypersurfaces. Although this topic has been extensively studied, many problems still remain open.

In this talk, I will present Lp estimates for maximal averages associated to hypersurfaces, with particular emphasis on their relationship to the decay rate of the Fourier transform of measures supported on the hypersurfaces.