Probability Seminar
Thursday, January 19, 2017, 4:15pm, UNC, 125 Hanes Hall
Michael Perlmutter (UNC)
Martingale Transforms and their Applications to Harmonic Analysis
Abstract:- Martingale transform methods are a powerful tool for the study of many operators of classical interest in harmonic analysis such as the Riesz transforms and the Beurling-Ahlfors transform. In particular, these methods allow us to transfer D.L. Burkholders sharp constant, p*-1, for the boundedness of martingale transforms to a large class of analytic operators. I will discuss the history of such methods and some of their limitations. I will then show how some of these obstacles can be overcome by a combination of probabilistic and analytic techniques.
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