PreprintCC0arXiv
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.
Related
- Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms
- Martingale Transforms and Compensated Bellman Estimates for Dunkl Riesz Transforms
- Sharp Realizability, Extremal Rigidity, and Injectivity Phenomena for Generalized Root Transforms on Hilbert Balls
- Young Parabolic PDEs and the Martingale Problem for Young SDEs
- Duality for a Martingale Transport Problem with Moment Constraints
BibTeX
@misc{vasyunin2026some,
title = {{Some extremal problem for martingale transforms. III}},
author = {Vasily Vasyunin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12719},
eprint = {2609.12719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12719},
note = {CC0},
}
RIS
TY - UNPB
TI - Some extremal problem for martingale transforms. III
AU - Vasily Vasyunin
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12719
UR - https://arxiv.org/abs/2609.12719
AB - 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.
ER -