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arXiv · 2604.11273

A twosided linear estimate and a dyadic reduction of the UMD Conjecture

Komla Domelevo·Stefanie Petermichl
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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.

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Komla Domelevo, Stefanie Petermichl. 2026-04-13. A twosided linear estimate and a dyadic reduction of the UMD Conjecture. https://arxiv.org/abs/2604.11273

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