Mathematics Dept.
  Events
Francesco DiPlinio
University of Virginia
Mon 25 Feb 2019, 3:00pm
Harmonic Analysis Seminar
MATH 126
Directional operators and the multiplier problem for the polygon
MATH 126
Mon 25 Feb 2019, 3:00pm-4:00pm

Abstract

I will discuss two recent results obtained in collaboration with I. Parissis (U Basque Country).  The first is a sharp L^2 estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth.
 

The second result is a sharp L^4 estimate for the Fourier multiplier associated to a polygon of N sides in R^2, and a sharp form of the two parameter Meyer's lemma. These results improve on the usual ones obtained via weighted norm inequalities and rely on a novel Carleson measure estimate for directional square functions of time-frequency nature.
hide
MIT
Mon 11 Mar 2019, 3:00pm
Harmonic Analysis Seminar
MATH 126
TBA
MATH 126
Mon 11 Mar 2019, 3:00pm-10:00am

Abstract

 
hide
Purdue
Mon 1 Apr 2019, 3:00pm
Harmonic Analysis Seminar
Math 126
TBA
Math 126
Mon 1 Apr 2019, 3:00pm-4:00pm

Abstract

 
hide