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In this paper, the  T  b  theorem of the inhomogeneous Besov and Triebel–Lizorkin spaces associated with a para-accretive function on homogeneous type spaces is established. As an application, we obtain that the Riesz potential can be used as the lifting operator of these spaces.

The T b theorem for inhomogeneous Besov and Triebel–Lizorkin spaces and its application