Characterizations of $A_\infty$ Weights in Ergodic Theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929499630731264 |
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| author | Chen, Wei Wang, Jingyi |
| author_facet | Chen, Wei Wang, Jingyi |
| contents | We establish a discrete weighted version of Calderón-Zygmund decomposition from the perspective of dyadic grid in ergodic theory. Based on the decomposition, we study discrete $A_\infty$ weights. First, characterizations of the reverse Hölder's inequality and their extensions are obtained. Second, the properties of $A_\infty$ are given, specifically $A_\infty$ implies the reverse Hölder's inequality. Finally, under a doubling condition on weights, $A_\infty$ follows from the reverse Hölder's inequality. This means that we obtain equivalent characterizations of $A_{\infty}$. Because $A_{\infty}$ implies the doubling condition, it seems reasonable to assume the condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08896 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizations of $A_\infty$ Weights in Ergodic Theory Chen, Wei Wang, Jingyi Classical Analysis and ODEs Probability 28D05, 37A46 We establish a discrete weighted version of Calderón-Zygmund decomposition from the perspective of dyadic grid in ergodic theory. Based on the decomposition, we study discrete $A_\infty$ weights. First, characterizations of the reverse Hölder's inequality and their extensions are obtained. Second, the properties of $A_\infty$ are given, specifically $A_\infty$ implies the reverse Hölder's inequality. Finally, under a doubling condition on weights, $A_\infty$ follows from the reverse Hölder's inequality. This means that we obtain equivalent characterizations of $A_{\infty}$. Because $A_{\infty}$ implies the doubling condition, it seems reasonable to assume the condition. |
| title | Characterizations of $A_\infty$ Weights in Ergodic Theory |
| topic | Classical Analysis and ODEs Probability 28D05, 37A46 |
| url | https://arxiv.org/abs/2409.08896 |