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

Let \(\mathbb{G}\) be any Carnot group. We prove that if a convolution type singular integral associated with a \(1\)-dimensional Calderón-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}, \alph...

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Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: Chousionis, Vasileios, Li, Sean, Zimmerman, Scott
Format: Article
Language:English
Subjects:
Convolution
Integrals
Online Access:Get full text
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Summary:Let \(\mathbb{G}\) be any Carnot group. We prove that if a convolution type singular integral associated with a \(1\)-dimensional Calderón-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 \(\mathbb{G}\).
ISSN:2331-8422