Maximal averages and Radon transforms for two-dimensional hypersurfaces

Series: 
Analysis Seminar
Wednesday, October 25, 2017 - 13:55
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of Illinois, Chicago
Organizer: 
A general local result concerning L^p boundedness of maximal averages over 2D hypersurfaces is described, where p > 2. The surfaces are allowed to have either the traditional smooth density function or a singularity growing as |(x,y)|^{-t} for some 0 < t < 2. This result is a generalization of a theorem of Ikromov, Kempe, and Mueller. Similar methods can be used to show sharp L^p to L^p_a Sobolev estimates for associated Radon transform operators when p is in a certain interval containing 2.