Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915774144184320 |
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| author | Wang, Dinghuai |
| author_facet | Wang, Dinghuai |
| contents | By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values where the classical inequalities fail. As an important corollary, we obtain weak-type Hardy inequalities that hold true even in the critical dimension \(d = p\). The methods developed here are sufficiently flexible to handle homogeneous, non-homogeneous and anisotropic weights, providing a unified approach to various endpoint cases in interpolation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces Wang, Dinghuai Classical Analysis and ODEs Analysis of PDEs By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values where the classical inequalities fail. As an important corollary, we obtain weak-type Hardy inequalities that hold true even in the critical dimension \(d = p\). The methods developed here are sufficiently flexible to handle homogeneous, non-homogeneous and anisotropic weights, providing a unified approach to various endpoint cases in interpolation theory. |
| title | Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2602.04601 |