Dissertation es mathematic ae

In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (inhomogeneous) Besov and Triebel- Lizorkin spaces are independent of the choices of both (inhomogeneous) approximations of the identity with exponential decay and underlying spaces of distributions, and give some basic properties of these spaces. As applications, the authors show that some known function spaces coincide with certain special cases of Besov and Triebel-Lizorkin spaces and, moreover, obtain the boundedness of Calderon-Zygmund operators on these Besov and Triebel-Lizorkin spaces. All these results strongly depend on the geometrical properties, reflected via dyadic cubes, of the relevant space of homogeneous type. Compared with the known theory of these spaces on metric measure spaces, a major novelty of this article is that all results presented in this article get rid of the dependence on the reverse doubling assumption of the measure under study of the underlying space.