Sergi Arias Garcia: Some endpoint estimates for bilinear Coifman-Meyer multipliers

Abstract

In this talk we will review some known estimates for bilinear Coifman-Meyer multipliers and present some new results while acting on some endpoint spaces. More precisely, we will consider the case in which one of the arguments of the operator is fixed in the space of functions with local bounded mean oscillation, bmo, while the other one is either in a Lebesgue space or in the Hardy space \(H^1\).

The most natural bilinear operator, the product of two functions, is a particular instance of Coifman-Meyer multipliers. As an application of the main results, we will also present some estimates on products of functions in local bmo with functions in either a Lebesgue space or in the local Hardy space \(h^1 \), as well as related Kato-Ponce-type inequalities.