Multipoint Characterization of Higher-Order Sobolev Spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911735986782208 |
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| author | Kurowski, Kacper |
| author_facet | Kurowski, Kacper |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00897 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multipoint Characterization of Higher-Order Sobolev Spaces Kurowski, Kacper Functional Analysis 46E35 (Primary) 46E36 (Secondary) 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. |
| title | Multipoint Characterization of Higher-Order Sobolev Spaces |
| topic | Functional Analysis 46E35 (Primary) 46E36 (Secondary) |
| url | https://arxiv.org/abs/2606.00897 |