Singular integrals on carleson measure spaces CMO~p on product spaces of homogeneous type

摘要

In the setting of product spaces M of homogeneous type, we prove that every product non-isotropic smooth (NIS) operator T is bounded on the generalized Carleson measure space CMO~p(M) of Han, Li and Lu for p0 < p < 1. Here p0 depends on the homogeneous dimensions of the measures on factors of the product space M and on the regularity of the quasi-metrics on factors of M. The L~p boundedness for 1 < p < ∞ of the class of NIS operators was developed in both the one-parameter case and the multiparameter case by Nagel and Stein, and the Hp boundedness was established in the multiparameter case by Han, Li and Lu.