072  Berichtsreihe des Mathematischen Seminars der Universität Kiel  
Yongsheng Han, Detlef Müller, Dachun Yang:Besov and TriebelLizorkin Spaces on Metric Measure Spaces Modeled on CarnotCaratheodory SpacesIn this paper, we work on RDspaces $\cx$, i.\,e., spaces of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\cx.$ An important class of RDspaces is provided by CarnotCarath\'eodory spaces with a doubling measure. By constructing an approximation of the identity with bounded support of Coifman type, we develop a theory of Besov and TriebelLizorkin spaces on the underlying spaces. In particular, this includes a theory of Hardy spaces $\hx$ and local Hardy spaces $\shx$ on RDspaces, which appears to be new in this setting. Moreover, we prove boundedness results on these Besov and TriebelLizorkin spaces for classes of singular integral operators, which include nonisotropic smoothing operators of order zero in the sense of Nagel and Stein that appear in estimates for solutions of the KohnLaplacian on certain classes of model domains in $\cc^N$. Our theory applies in a wide range of settings, for instance, to Ahlfors $n$regular metric measure spaces, Lie groups of polynomial volume growth, compact CarnotCarath\'eodory (also called subRiemannian) manifolds and to boundaries of certain unbounded model domains of polynomial type in $\cc^N$ appearing in the work of Nagel and Stein. Mathematics Subject Classification (1991): Primary 42B35; Secondary 46E35, 42B25, 42B20, 42B30, 43A99 Keywords: space of homogeneous type, RDspace, CarnotCaratheodory space, Ahlfors $n$regular metric measure space, Lie group of polynomial volume growth, unbounded model domain of polynomial type, Besov space, TriebelLizorkin space, Hardy space, BMO, test function, approximation of the identity, Calderon reproducing formula, LittlewoodPaley function, singular integral operator, frame, interpolation, dual space

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