Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces*

Abstract

Under the assumption that $\mu$ is a non-doubling measure on ${\Bbb R}^d$, the authors obtain the boundedness of commutators generated by Calder\'on-Zygmund operators or fractional integrals with Lipschitz functions in the Lebesgue space and the Hardy space.