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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2301.05857 |
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| _version_ | 1866911846780370944 |
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| author | Ju, Jie Chen, Wei Cui, Jingya Zhang, Chao |
| author_facet | Ju, Jie Chen, Wei Cui, Jingya Zhang, Chao |
| contents | Grafakos systematically proved that $A_\infty$ weights have different characterizations for cubes in Euclidean spaces in his classical text book. Very recently, Duoandikoetxea, Mart\'ın-Reyes, Ombrosi and Kosz discussed several characterizations of the $A_{\infty}$ weights in the setting of general bases. By conditional expectations, we study $A_\infty$ weights in martingale spaces. Because conditional expectations are Radon-Nikodým derivatives with respect to sub$\hbox{-}σ\hbox{-}$fields which have no geometric structures, we need new ingredients. Under a regularity assumption on weights, we obtain equivalent characterizations of the $A_{\infty}$ weights. Moreover, using weights modulo conditional expectations, we have one-way implications of different characterizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizations of $A_\infty$ Weights in Martingale Spaces Ju, Jie Chen, Wei Cui, Jingya Zhang, Chao Probability 60G46, 60G48, 60G42 Grafakos systematically proved that $A_\infty$ weights have different characterizations for cubes in Euclidean spaces in his classical text book. Very recently, Duoandikoetxea, Mart\'ın-Reyes, Ombrosi and Kosz discussed several characterizations of the $A_{\infty}$ weights in the setting of general bases. By conditional expectations, we study $A_\infty$ weights in martingale spaces. Because conditional expectations are Radon-Nikodým derivatives with respect to sub$\hbox{-}σ\hbox{-}$fields which have no geometric structures, we need new ingredients. Under a regularity assumption on weights, we obtain equivalent characterizations of the $A_{\infty}$ weights. Moreover, using weights modulo conditional expectations, we have one-way implications of different characterizations. |
| title | Characterizations of $A_\infty$ Weights in Martingale Spaces |
| topic | Probability 60G46, 60G48, 60G42 |
| url | https://arxiv.org/abs/2301.05857 |