** Weighted BMO Type Spaces Associated to Admissible Functions and Applications **

*Nguyen Ngoc Trong, Nguyen Thanh Tung *

**Abstract**

Let *ρ* be an admissible function on an RD-space *X*. The main aim of this paper is to establish the theory of weighted bounded mean oscillation (BMO) type spaces *g*-functions, and fractional integrals on these weighted BMO type spaces. Our findings extend well-known results in Bongioanni et al. (J. Math. Anal. Appl. **348**, 12–27, 2008), Liu et al. (Math. Nachr. **357**, 1–35, 2012), Yang and Zhou (Trans. Am. Math. Soc. **363**, 1197–1239, 2011), Yang et al. (Commun. Pure Appl. Anal. **9**, 779–812, 2010), and Yang et al. (Nagoya Math. J. **198**, 77–119, 2010).