Centered Hardy-Littlewood maximal function on hyperbolic spaces, $p > 1$

TL;DR

This paper establishes dimension-free $L^p$ bounds for the centered Hardy-Littlewood maximal function on hyperbolic spaces, extending understanding of maximal inequalities in non-Euclidean geometries.

Contribution

It provides the first proof of dimension-free bounds for the centered Hardy-Littlewood maximal function on hyperbolic spaces for all $p > 1$, both real and complex.

Findings

Dimension-free $L^p$ bounds proved for hyperbolic spaces

Results hold for both real and complex hyperbolic spaces

Extends maximal function theory to non-Euclidean geometries

Abstract

In this paper, we prove $L^p$ ($p > 1$) dimension free bounds for the centered Hardy-Littlewood maximal function on real or complex hyperbolic spaces.