# Off-diagonal estimates for cube skeletons maximal operators

## TL;DR

This paper develops off-diagonal estimates for a geometric maximal operator related to k-skeletons in Euclidean space, using interpolation and geometric analysis techniques.

## Contribution

It introduces new off-diagonal bounds for skeleton-based maximal operators by combining geometric insights with interpolation methods.

## Key findings

- Established off-diagonal estimates for skeleton maximal operators.
- Connected geometric skeleton properties with harmonic analysis techniques.
- Extended off-diagonal estimate methods from circular to skeleton configurations.

## Abstract

We provide off-diagonal estimates for a maximal operator arising from a geometric problem of estimating the size of certain geometric configuration of k- skeletons in $\mathbb{R}^n$. This is achieved by interpolating a weak-type endpoint estimate with the known diagonal bounds. The endpoint estimate is proved by combining a geometric result about k-skeletons and adapting an argument used to prove off-diagonal estimates for the circular maximal function in the plane.