Heat extensions, optimal atomic decompositions and Sobolev embeddings in presence of symmetries on manifolds

Abstract.

Our purpose is twofold. We give the heat semi-group characterization of spaces of Besov and Triebel-Lizorkin types defined on Riemannian manifolds of bounded geometry. Moreover we study boundedness and compactness of Sobolev embeddings of the spaces in presence of symmetries. To make it possible we first construct an optimal atomic decomposition for the above function spaces.