Morrey spaces on weighted homogeneous trees

In this paper, the authors construct the Morrey spaces ${\mathcal{M}}_p^{\lambda }(\mathcal{V})$ 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 ${\mathcal{M}}_p^{\lambda }(\mathcal{V})$ is established.