Singular integrals on C^1,α intrinsic graphs in step 2 Carnot groups

2025/03/12 by Vasileios Chousionis, Sean Li, Chousionis, Vasileios +3
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.09779

openalex publication_date 2025/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study singular integral operators induced by Calderón-Zygmund kernels in any step-2 Carnot group \mathbbG. We show that if such an operator satisfies some natural cancellation conditions then it is L² bounded on all intrinsic graphs of C^1,α functions over vertical hyperplanes that do not have rapid growth at ∞. In particular, the result applies to the Riesz operator R induced by the kernel R(z)= ∇_\mathbbG Γ(z), z∈ \mathbbG\backslash \0\, the horizontal gradient of the fundamental solution of the sub-Laplacian. The L² boundedness of R is connected with the question of removability for Lipschitz harmonic functions. As a corollary of our result, we infer that closed subsets of the intrinsic graphs mentioned above are non-removable.

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