Cody Stockdale will discuss a sparse bound for Haar multiplier operators and how it can be used to obtain inequalities and compactness results on weighted spaces today at 4:10 p.m. via Zoom.
Abstract: The theory of weighted inequalities is of central importance in modern harmonic analysis. In this area, one studies the weights for which a given operator acts boundedly on the corresponding weighted Lebesgue space, as well as the dependence of the bound on the weight. For many operators, such as maximal functions and the Hilbert transform, the weighted boundedness is characterized by the weight satisfying Muckenhoupt’s A_p condition. Recently, bounds by sparse operators revolutionized the study of weighted inequalities—researchers now know inequalities for many more operators, frequently with optimal dependence on the weight and with simpler proofs.