Discrete maximal operators over surfaces of higher codimension

2020/06/17 by Theresa C. Anderson, Anderson, Theresa C., Eyvindur A. Palsson +3
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2006.09968

openalex publication_date 2020/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research. Here we unite these themes to study discrete analogues of operators involving higher (intermediate) codimensional integration. We consider a maximal operator that averages over triangular configurations and prove several bounds that are close to optimal. A distinct feature of our approach is the use of multilinearity to obtain nontrivial ℓ¹-estimates by a rather general idea that is likely to be applicable to other problems.

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