The two-weight fractional Poincaré-Sobolev sandwich
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918436914855936 |
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| author | Lorist, Emiel Wagenaar, Carel |
| author_facet | Lorist, Emiel Wagenaar, Carel |
| contents | We establish a two-weight fractional Poincaré-Sobolev sandwich, consisting of a two-weight fractional Poincaré-Sobolev inequality and a two-weight embedding from the first-order Sobolev space to a Triebel-Lizorkin space defined via a difference norm. Our constants are asymptotically sharp as the fractional parameter approaches $1$. Our results are new even in the one-weight case.
For each inequality we give explicit quantitative dependence on Muckenhoupt weight characteristics and treat both subcritical and critical regimes, the former via elementary methods and the latter via sparse domination. As one of our main tools, we establish a new sparse domination result for Triebel-Lizorkin difference norms. Our methods unify, simplify and significantly extend various earlier approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08416 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The two-weight fractional Poincaré-Sobolev sandwich Lorist, Emiel Wagenaar, Carel Classical Analysis and ODEs Analysis of PDEs 46E35, 42B25, 26D10 We establish a two-weight fractional Poincaré-Sobolev sandwich, consisting of a two-weight fractional Poincaré-Sobolev inequality and a two-weight embedding from the first-order Sobolev space to a Triebel-Lizorkin space defined via a difference norm. Our constants are asymptotically sharp as the fractional parameter approaches $1$. Our results are new even in the one-weight case. For each inequality we give explicit quantitative dependence on Muckenhoupt weight characteristics and treat both subcritical and critical regimes, the former via elementary methods and the latter via sparse domination. As one of our main tools, we establish a new sparse domination result for Triebel-Lizorkin difference norms. Our methods unify, simplify and significantly extend various earlier approaches. |
| title | The two-weight fractional Poincaré-Sobolev sandwich |
| topic | Classical Analysis and ODEs Analysis of PDEs 46E35, 42B25, 26D10 |
| url | https://arxiv.org/abs/2604.08416 |