Mathematical Sciences Department, Colloquium - Joris Roos, UMass Lowell "Spherical maximal functions and fractal dimensions of dilation sets" (SH 203)
11:00 am to 12:00 pm
Mathematical Sciences Department
Speaker: Joris Roos, UMass Lowell
Friday, March 31, 2023
11:00 am - 12:00 pm
Stratton Hall 203
Title: Spherical maximal functions and fractal dimensions of dilation sets
Abstract: This talk is about subtle properties of averages on spheres in two and higher-dimensional Euclidean space. Maximal spherical averages are a classic topic in harmonic analysis originating in questions on differentiability properties of functions. We consider maximal spherical averages with a supremum taken over a given dilation set. It turns out that the sharp Lp improving properties of such operators are closely related to fractal dimensions of the dilation set such as the Minkowski and Assouad dimensions. This leads to a surprising characterization of the closed convex sets which can occur as closure of the sharp Lp improving region of such a maximal operator.
This is joint work with Andreas Seeger.