Commutators of Calder\'on-Zygmund Operators and Bounded Mean Oscillation (or Factorization and Hardy Spaces)

Abstract: Calder\'on-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 Calder\'on-Zygmund operators and multiplication operators. In this talk, we will discuss some recent results about commutators of certain Calderon-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.

analysis of PDEsclassical analysis and ODEscomplex variablesdifferential geometrydynamical systemsfunctional analysismetric geometry

Audience: researchers in the topic

Analysis and Geometry Seminar