Mathematics > Functional Analysis
arXiv:2606.00897 (math)
[Submitted on 30 May 2026]
Abstract:In the paper, we prove a rather general characterization of higher-order Sobolev spaces. We show that the $k\mathrm{th}$-order regularity, where $k \in \mathbb{N}$, is captured via inequalities involving $2^k$-tuples of points. In fact, in full generality, the obtained results characterize higher-order Sobolev spaces based on Banach function spaces. Moreover, we show an analogous characterization of higher-order Hölder spaces. Finally, we propose a way to use the obtained results to define higher-order Sobolev and Hölder spaces on metric measure spaces.
Submission history
From: Kacper Kurowski [view email]
[v1]
Sat, 30 May 2026 21:18:23 UTC (86 KB)
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