The Spherical Maximal Function on the Free Two-step Nilpotent Lie Group

TL;DR

This paper proves the boundedness of a maximal function on a specific nilpotent Lie group, extending harmonic analysis tools to this non-commutative setting.

Contribution

It establishes the $L^p$-boundedness of the spherical maximal function on the free two-step nilpotent Lie group with the Korányi norm.

Findings

Proves $L^p$-boundedness for some $p$

Extends harmonic analysis to non-commutative groups

Analyzes maximal functions on nilpotent Lie groups

Abstract

We consider here the free two step nilpotent Lie group, provided with the homogeneous Kor\'anyi norm; we prove the $L^p$-boundedness of the maximal function corresponding to the homogeneous unit sphere, for some $p$.