An interpolation result for $A_1$ weights with applications to fractional Poincaré inequalities
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914772775075840 |
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| author | Drelichman, Irene |
| author_facet | Drelichman, Irene |
| contents | We characterize the real interpolation space between weighted $L^1$ and $W^{1,1}$ spaces on arbitrary domains different from $\mathbb{R}^n$, when the weights are positive powers of the distance to the boundary multiplied by an $A_1$ weight. As an application of this result we obtain weighted fractional Poincaré inequalities with sharp dependence on the fractional parameter $s$ (for $s$ close to 1) and show that they are equivalent to a weighted Poincaré inequality for the gradient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18453 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An interpolation result for $A_1$ weights with applications to fractional Poincaré inequalities Drelichman, Irene Classical Analysis and ODEs Primary: 46E35, Secondary: 46B70, 26D10 We characterize the real interpolation space between weighted $L^1$ and $W^{1,1}$ spaces on arbitrary domains different from $\mathbb{R}^n$, when the weights are positive powers of the distance to the boundary multiplied by an $A_1$ weight. As an application of this result we obtain weighted fractional Poincaré inequalities with sharp dependence on the fractional parameter $s$ (for $s$ close to 1) and show that they are equivalent to a weighted Poincaré inequality for the gradient. |
| title | An interpolation result for $A_1$ weights with applications to fractional Poincaré inequalities |
| topic | Classical Analysis and ODEs Primary: 46E35, Secondary: 46B70, 26D10 |
| url | https://arxiv.org/abs/2310.18453 |