Analysis Seminar: Multiplier Weak-Type Inequalities for the Maximal Operator

Abstract: We discuss a kind of weak-type inequality for the Hardy-Littlewood maximal operator that was first studied by Muckenhoupt and Wheeden. This formulation treats the weight for the image space as a multiplier, rather than a measure, leading to fundamentally different behavior; in particular, as shown by Muckenhoupt and Wheeden, the class of weights characterizing such inequalities is strictly larger than $A_p$. In this talk, I will present recent work on the full characterization of the weights for which these inequalities hold for the Hardy-Littlewood maximal operator. Connections to weak-type estimates for the Bergman projection on bounded simply connected planar domains will also be discussed.

Host: Alan Chang