$www.math.cornell.edu$

Peter Luthy

Ph.D. (2013) Cornell University

First Position

Chauvenet Postdoctoral Lecturer at Washington University in St. Louis

Dissertation

Bi-parameter Maximal Multilinear Operators

Advisor:

Camil Muscalu

Research Area:

harmonic analysis

Abstract: It is well known that estimates for maximal operators and questions of pointwise convergence are strongly connected. In recent years, convergence properties of so-called ‘non-conventional ergodic averages’ have been studied by a number of authors, including Assani, Austin, Host, Kra, Tao, and so on. In particular, much is known regarding convergence in L² of these averages, but little is known about pointwise convergence. In this spirit, we consider the pointwise convergence of a particular ergodic average and study the corresponding maximal trilinear operator (over R, thanks to a transference principle) which has a novel bi-parameter structure not previously seen.