BOUNDEDNESS OF MULTILINEAR COMMUTATORS OF CALDERÓN-ZYGMUND OPERATORS ON ORLICZ SPACES OVER NON-HOMOGENEOUS SPACES

Abstract

Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors prove that multilinear commutators of Calderón-Zygmund operators with RBMO($\mu$) functions are bounded on Orlicz spaces, especially, on $L^p(\mu)$ with $p \in (1,\infty)$. The weak type endpoint estimate of multilinear commutators of Calderón-Zygmund operators with Orlicz type functions in $Osc_{\exp L^r}(\mu)$ for $r \in [1,\infty)$ is also presented.