Mixed commutators and little product BMO

Abstract

We consider iterated commutators of multiplication by a symbol function and tensor products of Hilbert or Riesz transforms. We establish mixed BMO classes of symbols that characterize boundedness of these objects in L p . Little BMO and prod- uct BMO, big Hankel operators and iterated commutators are the base cases of our results. We use operator theoretical methods and existing profound results on iterated commutators for the Hilbert transform case, while the general result in several variables is obtained through the construction of a Journe operator that models the behavior of the multiple Hilbert transform. Upper estimates for commutators with paraproduct free Journe operators as well as weak factorisation results are proven.

Locations

• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF