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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2407.12098 |
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| _version_ | 1866909259200987136 |
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| author | Adimurthi Jana, Purbita Roy, Prosenjit |
| author_facet | Adimurthi Jana, Purbita Roy, Prosenjit |
| contents | We prove fractional boundary Hardy's inequality in dimension one for the critical case $sp =1$. Optimality of the inequality is obtained for any $p$. The extra logarithmic correction term appears in usual fashion. We also provide a concrete (workable) example of a sequence of smooth functions that converges to constant function in $W^{s,p}((0,1))$ for $sp=1$ and $p=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary fractional Hardy's inequality in dimension one: The critical case Adimurthi Jana, Purbita Roy, Prosenjit Analysis of PDEs We prove fractional boundary Hardy's inequality in dimension one for the critical case $sp =1$. Optimality of the inequality is obtained for any $p$. The extra logarithmic correction term appears in usual fashion. We also provide a concrete (workable) example of a sequence of smooth functions that converges to constant function in $W^{s,p}((0,1))$ for $sp=1$ and $p=2$. |
| title | Boundary fractional Hardy's inequality in dimension one: The critical case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.12098 |