The distance function and Lipschitz classes of mappings between metric spaces
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912492687458304 |
|---|---|
| author | Markovic, Marijan |
| author_facet | Markovic, Marijan |
| contents | We investigate when the local Lipschitz property of the real-valued function $g(z) = d_Y (f(z),A)$ implies the global Lipschitz property of the mapping $f:X\to Y$ between the metric spaces $(X,d_X)$ and $(Y,d_Y)$. Here, $d_Y(y,A)$ denotes the distance of $y\in Y$ from the non-empty set $\subseteq Y$. 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 K. 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 [14]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14508 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The distance function and Lipschitz classes of mappings between metric spaces Markovic, Marijan Complex Variables We investigate when the local Lipschitz property of the real-valued function $g(z) = d_Y (f(z),A)$ implies the global Lipschitz property of the mapping $f:X\to Y$ between the metric spaces $(X,d_X)$ and $(Y,d_Y)$. Here, $d_Y(y,A)$ denotes the distance of $y\in Y$ from the non-empty set $\subseteq Y$. 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 K. 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 [14]. |
| title | The distance function and Lipschitz classes of mappings between metric spaces |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2507.14508 |