Wavelet characterization of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type and its applications

In this article, the authors establish wavelet characterization of Besov and Triebel–Lizorkin spaces on a given space (X,d,μ) homogeneous type in sense Coifman Weiss. Moreover, introduce almost diagonal operators sequence X, obtain their boundedness. Using boundedness operators, molecular spaces. Applying characterization, further Littlewood–Paley characterizations X. The main novelty article is that all these results get rid dependence reverse doubling property μ also triangle inequality d, by fully using geometrical X expressed via its equipped quasi-metric dyadic reference points, cubes, wavelets.