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, 3:00pm4:00pm
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 timefrequency nature.
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MIT

Mon 11 Mar 2019, 3:00pm
Harmonic Analysis Seminar
MATH 126

TBA

MATH 126
Mon 11 Mar 2019, 3:00pm10:00am
Abstract
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Purdue

Mon 1 Apr 2019, 3:00pm
Harmonic Analysis Seminar
Math 126

TBA

Math 126
Mon 1 Apr 2019, 3:00pm4:00pm
Abstract
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