WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Intrinsically Hölder Sections in Metric Spaces
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Abstract: We introduce the notion of intrinsically Hölder graphs in metric spaces that generalized the one of intrinsically Lipschitz sections. This concept is relevant because it has many properties similar to Hölder maps but is profoundly different from them. We prove some relevant results as the Ascoli-Arzel`a compactness Theorem, Ahlfors-David regularity and the Extension Theorem for this class of sections. In the first part of this note, thanks to Cheeger theory, we define suitable sets in order to obtain a vector space over $$\mathbb{R}$$ or $$\mathbb{C}$$, a convex set and an equivalence relation for intrinsically Hölder graphs. These last three properties are new also in the Lipschitz case.
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Keywords: Hölder graphs, Ahlfors-David regularity, Extension theorem, Ascoli-Arzel`a compactness theorem, vector space, equivalence relation, Metric spaces
Pages: 723-730
DOI: 10.37394/23206.2024.23.74