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arXiv · 1912.13279

Singular integrals on $C^{1,\alpha}$ regular curves in Carnot groups

Vasileios Chousionis·Sean Li·Scott Zimmerman
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Abstract

Let $\mathbb{G}$ be any Carnot group. We prove that if a convolution type singular integral associated with a $1$-dimensional Calder\'on-Zygmund kernel is $L^2$-bounded on horizontal lines, with uniform bounds, then it is bounded in $L^p, p \in (1,\infty),$ on any compact $C^{1,\alpha}, \alpha \in (0,1],$ regular curve in $\mathbb{G}$.

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Vasileios Chousionis, Sean Li, Scott Zimmerman. 2019-12-31. Singular integrals on $C^{1,\alpha}$ regular curves in Carnot groups. https://arxiv.org/abs/1912.13279

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