Abstract
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 L2-bounded on horizontal lines, with uniform bounds, then it is bounded in Lp, p ∈ (1, ∞), on any compact C1, α, α ∈ (0, 1], regular curve in \(\mathbb{G}\).
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Chousionis, V., Li, S. & Zimmerman, S. Singular integrals on C1,α regular curves in Carnot groups. JAMA 146, 299–326 (2022). https://doi.org/10.1007/s11854-021-0194-z
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DOI: https://doi.org/10.1007/s11854-021-0194-z