A massive wall in functional analysis just collapsed into a simple problem about discrete operators.
April 14, 2026
Original Paper
A twosided linear estimate and a dyadic reduction of the UMD Conjecture
arXiv · 2604.11273
The Takeaway
This reduces the complex UMD conjecture to a two-sided linear estimate of simple dyadic operators. It transforms a high-level theoretical bottleneck into a manageable, discrete mathematical task.
From the 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 $L^p$ 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.