Probability Seminar: Michael Perlmutter, UNC-CH
Department of Statistics and Operations Research
Martingale Transforms and their Applications to Harmonic Analysis
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. Burkholder’s 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.
Refreshments will be served at 3:45 in the 3rd floor lounge of Hanes Hall