Properties and applications of partial multiple weights for fractional integrals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918036415447040 |
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| author | Dinghuai, Wang Huicheng, Yin |
| author_facet | Dinghuai, Wang Huicheng, Yin |
| contents | In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation theorem for two types of off-diagonal estimates. Secondly, we establish some weighted estimates for fractional integrals associated with partial Muckenhoupt weights. As applications, several basic inequalities (including the Fefferman-Phong inequality, the degenerate Poincaré inequality and the Caffarelli-Kohn-Nirenberg inequality) related to partial Muckenhoupt weights are derived. Meanwhile, our results can give the characterization of the commutators of fractional integrals, which yields a partial answer to an open question proposed by D. Cruz-Uribe in the paper [D. Cruz-Uribe, Two weight inequalities for fractional integral operators and commutators, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017, 25-85]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_21007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties and applications of partial multiple weights for fractional integrals Dinghuai, Wang Huicheng, Yin Classical Analysis and ODEs Functional Analysis In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation theorem for two types of off-diagonal estimates. Secondly, we establish some weighted estimates for fractional integrals associated with partial Muckenhoupt weights. As applications, several basic inequalities (including the Fefferman-Phong inequality, the degenerate Poincaré inequality and the Caffarelli-Kohn-Nirenberg inequality) related to partial Muckenhoupt weights are derived. Meanwhile, our results can give the characterization of the commutators of fractional integrals, which yields a partial answer to an open question proposed by D. Cruz-Uribe in the paper [D. Cruz-Uribe, Two weight inequalities for fractional integral operators and commutators, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017, 25-85]. |
| title | Properties and applications of partial multiple weights for fractional integrals |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2505.21007 |