Georgia Institute of Technology College of Sciences

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.