Let Dμ be Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. Denote by M (Dμ) Möbius invariant function spaces generated by Dμ. In this paper, we investigate the relation among Dμ, M (Dμ) and some Möbius invariant function spaces, such as the space BMOA of analytic functions on the open unit disk with boundary values of bounded mean oscillation and the Dirichlet space. Applying the relation between BMOA and M (Dμ), under the assumption that the weight function K is concave, we characterize the function K such that QK = BMOA . We also describe inner functions in M (Dμ) spaces.
- Dirichlet spaces with superharmonic weights
- Möbius invariant function spaces
- inner functions