Averages over Discrete Spheres

Analysis Seminar
Wednesday, August 28, 2019 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 005
Michael Lacey – Georgia Tech – lacey@math.gatech.edu
Michael Lacey

Fine properties of spherical averages in the continuous setting include
$L^p$  improving estimates
and sparse bounds, interesting in the settings of a fixed radius, lacunary sets of radii, and the
full set of radii. There is a parallel theory in the setting of discrete spherical averages, as studied
by Elias Stein, Akos Magyar, and Stephen Wainger. We recall the continuous case, outline the
discrete case, and illustrate a unifying proof technique. Joint work with Robert Kesler, and
Dario Mena Arias.