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»ã±¨ÌáÒª£ºThe theory of tent spaces on R^n was introduced by Coifman, Meyer and Stein, including atomic decomposition, duality theory and so on. Russ generalized the atomic decomposition for tent spaces to the case of spaces of homogeneous type $(X,d,\mu)$. The main purpose of this paper is to extend the results of Coifman, Meyer, Stein and Russ to weighted version. More precisely, we obtain a $q$-atomic decomposition for the weighted tent spaces $T^p_{2,w}(X)$, where $0<p\leq 1, 1<q<\infty,$ and $w\in A_\infty$. As an application, we give an atomic decomposition for weighted Hardy spaces associated to nonnegative self-adjoint operators on $X$. This is a joint work with Dr. Liangchuan Wu.

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