Maximal functions with twisted structures, distribution inequality and applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915908099768320 |
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| author | Li, Ji Liang, Chong-Wei Wen, Chaojie Wu, Qingyan |
| author_facet | Li, Ji Liang, Chong-Wei Wen, Chaojie Wu, Qingyan |
| contents | Motivated by the geometric reduction of Cauchy--Szegő projections on quadratic surfaces of higher codimension (Nagel--Ricci--Stein, 2001) and recent developments on the real-variable theory adapted to twisted multiparameter structures (arXiv:2603.26119), we establish the Fefferman--Stein type distribution inequality relating the twisted area function and the twisted non-tangential maximal function over $\mathbb{R}^{2m}$. By deploying a recursive integration-by-parts argument involving the twisted gradient and Laplacian, and constructing smooth, compactly supported weight functions to absorb cross-derivative errors, we obtain the required estimate. As an application, we prove the uniform $L^1$ boundedness of the twisted maximal function on the twisted atoms and complete the maximal function characterization of the twisted Hardy space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00345 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal functions with twisted structures, distribution inequality and applications Li, Ji Liang, Chong-Wei Wen, Chaojie Wu, Qingyan Classical Analysis and ODEs Motivated by the geometric reduction of Cauchy--Szegő projections on quadratic surfaces of higher codimension (Nagel--Ricci--Stein, 2001) and recent developments on the real-variable theory adapted to twisted multiparameter structures (arXiv:2603.26119), we establish the Fefferman--Stein type distribution inequality relating the twisted area function and the twisted non-tangential maximal function over $\mathbb{R}^{2m}$. By deploying a recursive integration-by-parts argument involving the twisted gradient and Laplacian, and constructing smooth, compactly supported weight functions to absorb cross-derivative errors, we obtain the required estimate. As an application, we prove the uniform $L^1$ boundedness of the twisted maximal function on the twisted atoms and complete the maximal function characterization of the twisted Hardy space. |
| title | Maximal functions with twisted structures, distribution inequality and applications |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2604.00345 |