Monge-Ampere Equations and Bellman Functions: The Dyadic Maximal Operator

Document Type

Presentation

Presentation Date

6-12-2012

Abstract or Description

When proving a sharp inequality in a harmonic analysis setting, one can sometimes recast the problem as that of finding the corresponding Bellman function. These functions often arise as solutions of Monge-Ampere PDEs on problem-specific domains; in such a case, the optimizers in the inequality can be found using the straight-line characteristics of the equation. I will show how to find the Bellman function for one important example – the dyadic maximal operator on Lp. This function has been previously found by A. Melas in a different way. The approach presented can be generalized to other well-localized operators and function classes. Joint work with Leonid Slavin and Vasily Vasyunin.

Sponsorship/Conference/Institution

International Conference on Harmonic Analysis and Partial Differential Equations

Location

Madrid, Spain

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