鞅变换的某些极值问题. III
Some extremal problem for martingale transforms. III
AI总结：
本文延续前作，研究鞅变换极值问题中新的局部叶状结构（主口袋、中口袋及双线性区域），并通过三次多项式实例分析其出现，最终给出边界值为三次多项式时所有可能叶状结构的完整概述。
AI中文摘要：
本文是论文 arXiv:2401.00053 和 arXiv:2507.09332 的直接续篇。因此，本文既不重复引言部分，也不重复参考文献。然而，为方便读者，前两篇论文中被引用的公式在文末以原始编号的特别附录中给出。在本文中，我们研究了新的局部叶状结构：主口袋、中口袋以及若干双线性区域。通过进一步分析三次多项式实例，说明了此类局部叶状结构的出现。在文末，当边界值为三次多项式时，给出了可能叶状结构的完整概述。
英文摘要：
This paper is a direct continuation of papers arxiv:2401.00053 and arxiv:2507.09332. By this reason, neither the introductory part of the paper nor the bibliography are duplicated here. However, for the reader's convenience, the formulas from the previous papers that are referenced are given in a special addendum at the end of the paper under their original numbers. In this paper, we investigate new local foliations: major and medium pockets and several bilinearity regions. The appearance of such local foliations is illustrated by further analysis of examples with third-degree polynomials. At the end of the paper, a complete overview of possible foliations is given when the boundary values are third-degree polynomials.
