WEAK TYPE ESTIMATES FOR COMMUTATORS ON HERZ-TYPE SPACES

Abstract

We consider the commutator of Calder\'{o}n-Zygmund operator and multiplication operator by $b$, that is, the commutator of Coifman, Rochberg and Weiss. We study the boundedness of this operator on the Hardy spaces associated with Herz spaces. We show this commutator is bounded from $H\dot{K}^{\alpha, p}_q$ (Hardy pace) to $\dot{K}^{\alpha, p, \infty}_q$ (weak Herz space).