Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators
Year: 2026
Type: preprint
Abstract: Let $T$ be a convolution Calderón--Zygmund operator satisfying Hytönen's non-degeneracy condition. We prove that, for every $p\in(1,\infty)$ and $m\ge3$, there exists a positive constant $C$ such that, for any $t\in[1,\infty)$, \begin{equation*} \sup_{[W]_{\mathcal A_p}\le t} \|T\|_{L^p(W)\to L^p(W)} \ge C t^{1+\frac{1}{p(p-1)}}, \end{equation*} where the supremum is taken over all matrix weights $W:\ \mathbb R^n\to\mathbb C^{m\times m}$ with their weight constants $[W]_{\mathcal A_p}\le t$. If, in addition, the odd part of the kernel is non-degenerate (such as the Hilbert transform and the Riesz transforms), the same conclusion holds for every $m\ge2$.
Source: arXiv (Cornell University)
Authors: Bu, Fan, Yang, Dachun, Yuan, Wen
Institutions: Beijing Normal University, Beijing Normal University, Zhuhai
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5710692465, G5884157002, G6737089312
OpenAlex ID: W7214736485