One-sided Muckenhoupt weights and one-sided weakly porous sets in $\mathbb{R}$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916849386520576 |
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| author | Aimar, Hugo Gómez, Ivana Vargas, Ignacio Gómez Martín-Reyes, Francisco Javier |
| author_facet | Aimar, Hugo Gómez, Ivana Vargas, Ignacio Gómez Martín-Reyes, Francisco Javier |
| contents | In this work, we introduce the geometric concept of one-sided weakly porous sets in the real line and show that a set $E\subset\mathbb{R}$ satisfies $d(\cdot,E)^{-α}\in A_1^+(\mathbb{R})\cap L^1_\textrm{loc}(\mathbb{R})$ for some $α>0$ if and only if $E$ is right-sided weakly porous. Furthermore, we find that the property of being both left-sided and right-sided weakly porous is equivalent to the recent weakly porous condition discussed in the bibliography, which, in turn, was previously found to be intimately related to the usual class of Muckenhoupt weights $A_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-sided Muckenhoupt weights and one-sided weakly porous sets in $\mathbb{R}$ Aimar, Hugo Gómez, Ivana Vargas, Ignacio Gómez Martín-Reyes, Francisco Javier Classical Analysis and ODEs Metric Geometry 28A80, 28A75, 42B37 In this work, we introduce the geometric concept of one-sided weakly porous sets in the real line and show that a set $E\subset\mathbb{R}$ satisfies $d(\cdot,E)^{-α}\in A_1^+(\mathbb{R})\cap L^1_\textrm{loc}(\mathbb{R})$ for some $α>0$ if and only if $E$ is right-sided weakly porous. Furthermore, we find that the property of being both left-sided and right-sided weakly porous is equivalent to the recent weakly porous condition discussed in the bibliography, which, in turn, was previously found to be intimately related to the usual class of Muckenhoupt weights $A_1$. |
| title | One-sided Muckenhoupt weights and one-sided weakly porous sets in $\mathbb{R}$ |
| topic | Classical Analysis and ODEs Metric Geometry 28A80, 28A75, 42B37 |
| url | https://arxiv.org/abs/2411.19856 |