A twosided linear estimate and a dyadic reduction of the UMD Conjecture
Functional Analysis
2026-04-14 v1 Probability
Abstract
We define a time faithful dyadic shift operator of complexity one, that is an antisymmetric antiinvolution. We show that the Hilbert transform with values in a Banach space is bounded if and only if the dyadic shift is -- with a linear two sided norm dependence. The results reduce the famous UMD conjecture to a pair of simple dyadic operators.
Keywords
Cite
@article{arxiv.2604.11273,
title = {A twosided linear estimate and a dyadic reduction of the UMD Conjecture},
author = {Komla Domelevo and Stefanie Petermichl},
journal= {arXiv preprint arXiv:2604.11273},
year = {2026}
}
Comments
33 pages, 5 figures, version for submission. arXiv admin note: text overlap with arXiv:2303.12480