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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.01081 |
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| _version_ | 1866917655734124544 |
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| author | Li, Ji Liang, Chong-Wei Shen, Chun-Yen Wick, Brett D. |
| author_facet | Li, Ji Liang, Chong-Wei Shen, Chun-Yen Wick, Brett D. |
| contents | Part of the intrinsic structure of singular integrals in the Bessel setting is captured by Muckenhoupt-type weights. Anderson--Kerman showed that the Bessel Riesz transform is bounded on weighted $L^p_w$ if and only if $w$ is in the class $A_{p,λ}$. We introduce a new class of Muckenhoupt-type weights $\widetilde A_{p,λ}$ in the Bessel setting, which is different from $A_{p,λ}$ but characterizes the weighted boundedness for the Hardy--Littlewood maximal operators. We also establish the weighted $L^p$ boundedness and compactness, as well as the endpoint weak type boundedness of Riesz commutators. The quantitative weighted bound is also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Muckenhoupt-Type Weights and Quantitative Weighted Estimate in the Bessel Setting Li, Ji Liang, Chong-Wei Shen, Chun-Yen Wick, Brett D. Classical Analysis and ODEs Part of the intrinsic structure of singular integrals in the Bessel setting is captured by Muckenhoupt-type weights. Anderson--Kerman showed that the Bessel Riesz transform is bounded on weighted $L^p_w$ if and only if $w$ is in the class $A_{p,λ}$. We introduce a new class of Muckenhoupt-type weights $\widetilde A_{p,λ}$ in the Bessel setting, which is different from $A_{p,λ}$ but characterizes the weighted boundedness for the Hardy--Littlewood maximal operators. We also establish the weighted $L^p$ boundedness and compactness, as well as the endpoint weak type boundedness of Riesz commutators. The quantitative weighted bound is also established. |
| title | Muckenhoupt-Type Weights and Quantitative Weighted Estimate in the Bessel Setting |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2405.01081 |