Extrapolation and commutators of singular integrals

Abstract

l. Introduction

In these notes we shall present results concerning LP inequalities with different but related weights for commutators of singular and strongly singular integrals. These commutators turn out to be controlled by commutator of fractional order of the Hardy-Littlewood maximal operator. The boundedness properties are obtained by extrapolation from infinity. These notes are based mainly on [G-H-S-T].