Discrete maximal operators and pinned simplices

TL;DR

This paper establishes $ ext{L}^2$ bounds for discrete maximal operators linked to simplices, extending the theory of discrete spherical maximal operators to more general geometric configurations.

Contribution

It introduces new $ ext{L}^2$ estimates for discrete maximal operators associated with simplices, broadening the scope of discrete harmonic analysis.

Findings

Proves $ ext{L}^2$ bounds for discrete maximal operators.

Generalizes discrete spherical maximal operator results.

Enhances understanding of geometric averaging operators.

Abstract

We prove $\ell^2$ estimates for certain discrete maximal operators associated to simplices. These operators are generalizations of the discrete spherical maximal operator.