Singular integrals on Carleson measure spaces CMOp on product spaces of homogeneous type
Date
2013
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Li, J.
Ward, L.A.
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Proceedings of the American Mathematical Society, 2013; 141(8):2767-2782
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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.
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Copyright 2013 American Mathematical Society