# A family of Dirichlet-Morrey spaces

## TL;DR

This paper introduces a new family of Morrey-type spaces derived from weighted Dirichlet spaces, exploring their properties, boundary value characterizations, and operator behaviors.

## Contribution

It defines and analyzes a novel family of Morrey-type spaces associated with Dirichlet spaces, detailing their properties and operator interactions.

## Key findings

- Characterization in terms of boundary values
- Properties of the new Morrey-type spaces
- Behavior of integration and multiplication operators

## Abstract

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.