Nov 17, 2021

Commutators of Calderón-Zygmund Operators and Bounded Mean Oscillation

Brett D. Wick, Washington University in St. Louis

Abstract:

Calderón-Zygmund operators play an important role in partial differential equations and complex analysis.  Some problems in analysis benefit from an understanding of the commutation between certain operators or the factorization of functions from natural function spaces.  These topics all interact when studying the commutators of Calderón-Zygmund operators and multiplication operators.  In this talk, we will discuss some recent results about commutators of certain Calderón-Zygmund operators and BMO spaces and how these generate bounded operators on Lebesgue spaces.  Motivations and connections to operator theory and partial differential equations will be provided.  Versions of these results on the Heisenberg group, pseudoconvex domains with $C^2$ boundary, and other examples will be explained to show how the general theory carries over to many other settings.  This talk is based on joint collaborative work.