Speaker: Mike Frazier
Title: Poincare inequalities and Matrix weights
Abstract: The first talk will be an introduction to Poincare inequalities for analysts who don't have a background in PDE. We will explain how the simplest version of the Poincare inequality gives existence of weak solutions to Poisson's equation. We will then discuss sharp versions of the Poincare inequality and how they follow from mapping properties of the Riesz potential. For people in the PDE community, the first talk will be familiar and probably not worth their time, but it is background for the second talk, in which we present Hedberg's proof of the Poincare inequality using the Hardy-Littlewood maximal function, and sketch how that proof can be used to prove a version of Poincare's inequality for matrix weights in the A_p class.
Wednesday, January 22 at 2:30pm to 3:20pm
Ayres Hall, 112
1403 Circle Drive, Knoxville, TN 37996