LAUSR

Abstract Let D μ , p be a Dirichlet type space induced by a positive parameter p and a positive Borel measure μ on the open unit disk. Denote by M ( D μ , p ) the Mobius invariant function space generated by D μ , p . It is known that if the measure μ is finite, then M ( D μ , p ) is equal to the well-known Mobius invariant space Q p . In this paper, we investigate D μ , p and M ( D μ , p ) spaces when the measures μ are not necessarily finite. We give the relation between M ( D μ , p ) and the Bloch space. We characterize inner functions in M ( D μ , p ) spaces. We also consider a Carleson measure problem for D μ , p spaces.