The distance function and Lipschitz classes of mappings between metric spaces

We investigate when the local Lipschitz property of the real‐valued function implies the global Lipschitz property of the mapping between the metric spaces and . Here, denotes the distance of from the non‐empty set . As a consequence, we find that an analytic function on a uniform domain of a normed space belongs to the Lipschitz class if and only if its modulus satisfies the same condition; in the case of the unit disk this result is proved by Dyakonov. We use the recently established version of a classical theorem by Hardy and Littlewood for mappings between metric spaces. This paper is a continuation of the recent article by the author [Marković, J. Geom. Anal. 34 (2024), https://doi.org/10.48550/arXiv.2405.11509 ].