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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 CMOp( 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 Lp 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.

Singular integrals on Carleson measure spaces ${CMO}^p$ on product spaces of homogeneous type