Using Calderón's reproducing formulas and almost orthogonal estimates, the $T1$ theorem for the inhomogeneous Triebel–Lizorkin and Besov spaces on RD-spaces is obtained. As an application, new characterizations for these spaces with “half” the usual conditions of the approximate to the identity are presented.
"$T1$ theorem for inhomogeneous Triebel–Lizorkin and Besov spaces on RD-spaces and its application." Adv. Oper. Theory 3 (3) 522 - 537, Summer 2018. https://doi.org/10.15352/aot.1709-1236