Mk-Type Estimates for Multilinear Commutator of Singular Integral Operator on Space of Homogeneous Type

Abstract

In this paper, we prove the M^k-type inequality for multilinear commutator related to singular integral operator on space of homogeneous type. By using the M^k-type inequality, we obtain the weighted L^p-norm inequality and the weighted estimates on the generalized Morrey spaces for the multilinear commutator.

Key words and phrases. Multilinear commutator, singular integral operator, BMO, M^k-type estimates, Morrey spaces, A₁-weight. 

2000 Mathematics Subject Classification. 42B20, 42B25