PUB - Publikationen an der Universität Bielefeld

Let (M, rho, mu) be a metric measure space satisfying the volume doubling condition. Assume also that (M, rho, mu) supports a heat kernel satisfying the upper and lower Gaussian bounds. We study the problem of identity of two families of Besov spaces B-p,q(s) and B-p,q(s,L), where the former one is defined using purely the metric measure structure of M, while the latter one is defined by means of the heat semigroup associated with the heat kernel. We prove that the identity B-p,q(s) = B-p,q(s,L) holds for a range of parameters p, q, s given by some Hardy-Littlewood-Sobolev-Kato diagram.