Abstract
In this paper, the authors give some new characterizations of the inhomogeneous Besov spaces and inhomogeneous Triebel-Lizorkin spaces respectively over space of homogeneous type, and establish the Tb theorems for the boundedness of the Calderón-Zygmund singular integral operator with non-convolution kernel on these new inhomogeneous Besov and Triebel-Lizorkin spaces.
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