Sparse domination and the strong maximal function

Analysis Seminar
Wednesday, January 16, 2019 - 1:55pm
1 hour (actually 50 minutes)
Skiles 005
Brown University

There has been recent interest in sparse bounds for various operators that arise in harmonic analysis. Perhaps the most basic "sparse" result is a pointwise bound for the dyadic Hardy-Littlewood maximal function. It turns out that the direct analogue of this result does not hold if one adds an extra dilation parameter: the dyadic strong maximal function does not admit a pointwise sparse bound or a sparse bound involving L^1 forms (both of which hold in the one-parameter setting). The proof is based on the construction of a certain pair of extremal point sets. This is joint work with Jose Conde-Alonso, Yumeng Ou, and Guillermo Rey.