Upper Bound for Multi-parameter Iterated Commutators

Abstract

We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón-Zygmund operators. This result follows from a new proof of boundedness of iterated commutators in terms of the BMO norm of their symbol functions, using Hytönen's representation theorem of Calderón-Zygmund operators as averages of dyadic shifts. The proof introduces some new paraproducts which have BMO estimates.

25 pages

References in corpus (1)

• Some obstacles in characterising the boundedness of bi-parameter singular integrals

Cited by in corpus (6)

• Bilinear Calderón-Zygmund theory on product spaces
• Two-weight commutator estimates: general multi-parameter framework
• Modern singular integral theory with mild kernel regularity
• Dyadic representation and boundedness of non-homogeneous Calderón--Zygmund operators with mild kernel regularity
• Product BMO, little BMO and Riesz Commutators in the Bessel setting
• Bloom type upper bounds in the product BMO setting