A twosided linear estimate and a dyadic reduction of the UMD Conjecture
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911588292755456 |
|---|---|
| author | Domelevo, Komla Petermichl, Stefanie |
| author_facet | Domelevo, Komla Petermichl, Stefanie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A twosided linear estimate and a dyadic reduction of the UMD Conjecture Domelevo, Komla Petermichl, Stefanie Functional Analysis Probability 46B20 (Primary) 60G42, 60G44, 65C30 (Secondary) 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. |
| title | A twosided linear estimate and a dyadic reduction of the UMD Conjecture |
| topic | Functional Analysis Probability 46B20 (Primary) 60G42, 60G44, 65C30 (Secondary) |
| url | https://arxiv.org/abs/2604.11273 |