  To each weighted Dirichlet space $\mathcal{D}_p$, $0<p<1$, we associate a
family of Morrey-type spaces ${\mathcal{D}}_p^{\lambda}$, $0< \lambda < 1$,
constructed by imposing growth conditions on the norm of hyperbolic translates
of functions. We indicate some of the properties of these spaces, mention the
characterization in terms of boundary values, and study integration and
multiplication operators on them.
