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arXiv · 2609.33560

Sharp Matrix $\mathcal A_p$ lower bounds for general non-degenerate convolution Calderón--Zygmund operators

Fan Bu·Dachun Yang·Wen Yuan
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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 every matrix dimension $m\ge3$, 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*} If, in addition, the odd part of the kernel is non-degenerate (as for the Hilbert transform and the Riesz transforms), the same conclusion holds for every $m\ge2$.

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Fan Bu, Dachun Yang, Wen Yuan. 2026-09-27. Sharp Matrix $\mathcal A_p$ lower bounds for general non-degenerate convolution Calderón--Zygmund operators. https://arxiv.org/abs/2609.33560

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