Weighted fractional Hardy-Sobolev and Hardy-Sobolev-Maz'ya inequalities with singularities on flat submanifold
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915702314631168 |
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| author | Kijaczko, Michał Sahu, Vivek |
| author_facet | Kijaczko, Michał Sahu, Vivek |
| contents | We investigate the sharp constant for weighted fractional Hardy inequalities with the singularity on a flat submanifold of codimension $k$, where $1\leq k<d$. We also prove a weighted fractional Hardy inequality with a remainder. Using this result, we extend and derive a weighted version of the fractional Hardy-Sobolev-Maz'ya inequality with singularities on a flat submanifold. Furthermore, we obtain a weighted logarithmic fractional Hardy-Sobolev-Maz'ya inequality in the case of a singularity at the origin and we show that in this case, the fractional Hardy-Sobolev-Maz'ya inequality does not hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted fractional Hardy-Sobolev and Hardy-Sobolev-Maz'ya inequalities with singularities on flat submanifold Kijaczko, Michał Sahu, Vivek Analysis of PDEs 46E35, 39B72, 26D15 We investigate the sharp constant for weighted fractional Hardy inequalities with the singularity on a flat submanifold of codimension $k$, where $1\leq k<d$. We also prove a weighted fractional Hardy inequality with a remainder. Using this result, we extend and derive a weighted version of the fractional Hardy-Sobolev-Maz'ya inequality with singularities on a flat submanifold. Furthermore, we obtain a weighted logarithmic fractional Hardy-Sobolev-Maz'ya inequality in the case of a singularity at the origin and we show that in this case, the fractional Hardy-Sobolev-Maz'ya inequality does not hold. |
| title | Weighted fractional Hardy-Sobolev and Hardy-Sobolev-Maz'ya inequalities with singularities on flat submanifold |
| topic | Analysis of PDEs 46E35, 39B72, 26D15 |
| url | https://arxiv.org/abs/2503.19057 |