Abstract
<div class="line" id="line-19"> 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.</div><div class="line" id="line-32"> <br/></div><div class="line" id="line-28"> 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.</div>
| Original language | American English |
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| State | Published - Jun 12 2012 |
| Event | International Conference on Harmonic Analysis and Partial Differential Equations - Madrid, Spain Duration: Jun 12 2012 → … |
Conference
| Conference | International Conference on Harmonic Analysis and Partial Differential Equations |
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| Period | 06/12/12 → … |
Keywords
- Bellman functions
- Dyadic maximal operator
- Monge-Ampere equations
DC Disciplines
- Mathematics