Some extremal problem for martingale transforms. III

Abstract

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.