Singular spherical maximal operators on a class of degenerate two-step nilpotent Lie groups

2022/07/26 by Naijia Liu, Lixin Yan, Liu, Naijia +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2207.12725

openalex publication_date 2022/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G≅ℝ^d \ltimes ℝ be a finite-dimensional two-step nilpotent group with the group multiplication (x,u)⋅(y,v)→(x+y,u+v+x^TJy) where J is a skew-symmetric matrix satisfying a degeneracy condition with 2≤ \rm rank J 0|∫_Σ f(x-ty, u- t x^TJy) dμ(y)|, where Σ is a smooth convex hypersurface and dμ is a compactly supported smooth density on Σ such that the Gaussian curvature of Σ is nonvanishing on supp dμ. In this paper we prove that when d≥ 4, the maximal operator \frak M is bounded on L^p(G) for the range (d-1)/(d-2)

Cited by

• Problems on spherical maximal functions
• Failure of stability of a maximal operator bound for perturbed Nevo--Thangavelu means

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