Jonathan Hickman

Ellipsoidal maximal function

Stein’s spherical maximal function is a singular variant of the classical Hardy–Littlewood maximal function, formed by taking maximal averages over concentric spheres. In recent years the study of such geometric maximal functions has flourished: many new techniques and results have become available, and the theory itself has found new and important applications. A typical problem is to prove an analogue of the Hardy—Littlewood maximal function in this setting: that is, determine the range of Lp for which a given maximal operator is bounded. In this talk, I will discuss a multiparameter variant of the spherical maximal function, formed by taking maximal averages over ellipsoids. Joint with Joshua Zahl.