Por Joris Roos (University of Edinburgh).
In this talk we will consider spherical maximal operators in Euclidean space with a supremum taken over a given dilation set. It turns out that the sharp $L^p$ improving properties of such operators are closely related to fractal dimensions of the dilation set such as the Minkowski and Assouad dimensions.
At the center of the talk will be a simple characterization of the closed convex sets which can occur as closure of the sharp $L^p$ improving region of such a maximal operator.
This is joint work with Andreas Seeger. Time permitting, we will also discuss some ongoing work and further directions.
Transmissão via Zoom (pw: lisbonwade).
The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.
