Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application5225375707210.15352/aot.1709-1236ENFanghui LiaoZongguang LiuChina University of Mining and Technology(Beijing)Hongbin WangJournal Article20170922Using Calder'{o}n'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.http://www.aot-math.org/article_57072_888f8c2b8da0ea7fac2ff9eeb211dc2a.pdf