Georgia Institute of Technology College of Sciences

This seminar has beeb cancelled and will be rescheduled next year.  We discuss a kind of weak type inequality for the Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operators that was first studied by Muckenhoupt and Wheeden and later by Sawyer. This formulation treats the weight for the image space as a multiplier, rather than a measure, leading to fundamentally different behavior. Such inequalities arise in the generalization of weak-type spaces to the matrix weighted setting and find applications in scalar two-weight norm inequalities via interpolation with change of measures. In this talk, I will discuss quantitative estimates obtained for $A_p$ weights, $p > 1$, that generalize those results obtained by Cruz-Uribe, Isralowitz, Moen, Pott and Rivera-Ríos for $p = 1$. I will also discuss an endpoint result for the Riesz potentials.