VECTOR VALUED COMMUTATORS ON NON-HOMOGENEOUS SPACES

Abstract

Let $\mu$ be a Borel measure on $\mathbb{R}^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(Q) \leq c_0 l(Q)^n$ for any cube $Q \subset \mathbb{R}^d$ with sides parallel to the coordinate axes and for some fixed $n$ with $0 \lt n \leq d$. This paper is to develop the vector valued commutator theory in the context of the non-thomogeneous spaces. As an application, the boundedness of the maximal commutator of any Calderón-Zygmund operator on the non-homogeneous space with a $RBMO(\mu)$ function introduced by Tolsa in [9] is obtained.