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arXiv · 2604.00345

Maximal functions with twisted structures, distribution inequality and applications

Ji Li·Chong-Wei Liang·Chaojie Wen·Qingyan Wu
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Abstract

Motivated by the geometric reduction of Cauchy--Szeg\H{o} 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.

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Ji Li, Chong-Wei Liang, Chaojie Wen, Qingyan Wu. 2026-04-01. Maximal functions with twisted structures, distribution inequality and applications. https://arxiv.org/abs/2604.00345

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