Title and Abstract

13th, 14:30 - 15:30

Local smoothing and maximal estimates for codimension two averages in R^4

This talk concerns averaging operators associated with dilations of two-dimensional surfaces in R^4. We study local smoothing and L^p-improving estimates for these operators, and show that the boundedness range for the associated maximal averages depends on the curvature structure of the underlying surface. In particular, we compare two model nondegenerate surfaces whose Hessian matrices have different rank properties, leading to different sharp L^p-improving ranges. This is joint work with Seheon Ham.