PDE Real Analysis Seminar

Seminar information archive ~02/28Next seminarFuture seminars 02/29~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2009/06/24

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Winston Ou (Scripps College / currently visiting assistant professor at Keio University)
Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights
[ Abstract ]
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\\infty$, and then present a few related problems.