Morrey spaces on weighted homogeneous trees

In this paper, the authors construct the Morrey spaces $ \mathcal{M}^{\lambda}_{p}(\mathcal{V}) $ on the metric measure spaces $ (\mathcal{V}, d, \mu) $ and explore their associated properties. Here, $ (\mathcal{V}, d, \mu) $ refers to metric measure spaces composed of infinite homogeneous trees $ T $ equipped with the standard graph metric $ d $ and a weighted measure $ \mu $. As applications, the boundedness of the maximal operator and the fractional maximal operator related to admissible trapezoids on the Morrey spaces $\mathcal{M}^\lambda_p(\mathcal{V})$ is established.