Wiley
The distance function and Lipschitz classes of mappings between metric spaces
AbstractWe 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...
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2025
Marijan Marković
World Scientific Pub Co Pte Ltd
A condition equivalent to the Hölder continuity of harmonic functions on unbounded Lipschitz domains
Our main result concerns the behavior of bounded harmonic functions on a domain in [Formula: see text] which may be represented as a strict epigraph of a Lipschitz function on [Formula: see text]. Generally speaking, the result says that the Hölder continuity of a harmonic function on such a domain is equivalent to the uniform Hölder continuity along the straight lines determined by the vector [Formula: see text], where [Formula: see text] is the base of standard vectors in [Formula: see text]....
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2025
Marijan Marković