The author first establishes the reduced T1 theorems for Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. Using these T1 theorems, the author proves that an operator of Bessel potential type can be used as the lifting operator of these spaces.
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Dachun Yang, T1 Theorems on Besov and Triebel-Lizorkin Spaces on Spaces of Homogeneous Type and Their Applications. Z. Anal. Anwend. 22 (2003), no. 1, pp. 53–72DOI 10.4171/ZAA/1132