MOBIUS INVARIANT FUNCTION SPACES AND DIRICHLET SPACES WITH SUPERHARMONIC WEIGHTS

Let D-mu be Dirichlet spaces with superharmonic weights induced by positive Borel measures mu on the open unit disk. Denote by M(D-mu) Mobius invariant function spaces generated by D-mu. In this paper, we investigate the relation among D-mu ,M(D-mu) and some Mobius 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(D-mu), under the assumption that the weight function K is concave, we characterize the function K such that Q(K) = BMOA. We also describe inner functions in M(D-mu) spaces.