发表机构
School of Mathematical Sciences, Xiamen University（厦门大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有限离散环面上坐标反对径差的标量线性分解与散度提升，证明最优正则范数为 m，并通过度量余型不等式获得一致有界的非线性提升。
AI 中文摘要
我们研究了有限离散环面上坐标反对径差通过符号增量的标量线性分解，以及相应的伴随散度提升。在边长为 \\(2m\\) 且 \\(m\\) 为偶数的环面上，两种分解的最优正则范数均为 \\(m\\)。商空间对偶性将最优非线性提升常数与相应的 Banach 值差常数等同起来。与 Cheng 和 Xiang 共同建立的尖锐 \\(L_1\\) 度量余型不等式随后产生了 \\(\ell_\infty^N\\) 值的非线性提升，在尖锐度量余型尺度上具有一致界，而归一化标量线性提升的最优正则范数随环面的维度增长。
英文摘要
We study scalar linear factorizations of coordinate antipodal differences through sign increments on finite discrete tori and the corresponding adjoint divergence liftings. On tori of side length \(2m\) with \(m\) even, the optimal regular norms of both factorizations are \(m\). Quotient-space duality identifies the optimal nonlinear lifting constant with the corresponding Banach-valued difference constant. A sharp \(L_1\) metric-cotype inequality established jointly with Cheng and Xiang then yields \(\ell_\infty^N\)-valued nonlinear liftings with a uniform bound at the sharp metric-cotype scales, whereas the optimal regular norms of the normalized scalar linear liftings grow with the dimension of the torus.
Comments11 pages
