Analysis Seminar/3rd Year Requirement: "Weighted Inequalities for Haar multipliers"
Speaker: Claire Huang, Washington University in Saint Louis
Abstract: A measure on R^n is called “dyadic doubling” if the measure ratio of any dyadic parent and its dyadic child is uniformly bounded. This property enables a stopping time argument presented by Katz and Pereyra in their 1998 survey on the L^p boundedness of Haar multipliers. Highly inspired by these two authors’ work, this presentation focuses on extending their results to weighted spaces. In particular, we are interested in the L^p boundedness of Haar multipliers with respect to weights in dyadic Muckenhoupt classes, as they guarantee dyadic doubling, and the closely related weights in dyadic reverse Holder classes.
Host: Brett Wick