2022/05/05 by Daniela Di Donato, Di Donato, Daniela
Mathematics · Computer Science · #Fixed Point Theorems Analysis #Optimization and Variational Analysis #Advanced Banach Space Theory
paper · pdf · doi:10.48550/arxiv.2205.02688
We introduce a notion of intrinsically Hölder graphs in metric spaces. Following a recent paper of Le Donne and the author, we prove some relevant results as the Ascoli-Arzelà 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 \R or \C, a convex set and an equivalence relation for intrinsically Hölder graphs. These last three properties are new also in the Lipschitz case. Throughout the paper, we use basic mathematical tools.