The paper is devoted to the spaces of generalized smoothness on so-called h–sets. First we find the quarkonial representations of isotropic spaces of generalized smoothness on R and on an h–set. Then we investigate the representations of such spaces via differences, which are very helpful when we want to find an explicit representation of the domain of a Dirichlet form on h–sets. We prove that ...

2 Tau-function on spaces of Abelian differentials over Riemann surfaces 7 2.1 Spaces of holomorphic differentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Variational formulas on Hg(k1, . . . , kM ) . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Basic Beltrami differentials for Hg(k1, . . . , kM ) . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Definition of...

We investigate the function theory on function spaces on a dyadic tree which model Dirichlet spaces of holomorphic functions. Most of the specific questions addressed deal with Carleson measures on those spaces.