Workshop on Discrete Methods in Ergodic Theory

Title: On the extremizers of a certain L^p norm inequality
Speaker: Michael Christ
Speaker Info: University of California, Berkeley
Brief Description:
Special Note:

Over the last few decades, a vast literature has developed concerning the mapping properties, in the scale of L^p spaces, of linear integral operators which involve singularities and/or curvature. Some of these inequalities have been established by exploiting a combinatorial perspective. There are natural inverse problems: Characterize those functions which extremize the inequalities up to bounded factors; determine whether extremizers exist; identify these if possible; determine their quantitative and qualitative properties in cases when identification is not possible. I will outline a series of works on these problems, for one of the most canonical of the Radon-like transforms. The most recent result is that extremizers for this particular inequality are infinitely differentiable. This is established via analysis of regularity of solutions of a certain nonlinear Euler-Lagrange equation. The main tool is a new family of weighted L^p norm inequalities. (joint work with Qingying Xue)
Date: Friday, February 25, 2011
Time: 3:30pm
Where: Chambers Hall, Downstairs
Contact Person: Bryna Kra
Contact email: kra@math.nortwestern.edu
Contact Phone:
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