Littlewood-Paley characterization of H\"older-Zygmund spaces on stratified Lie groups

TL;DR

This paper provides a Littlewood-Paley characterization of H"older-Zygmund spaces on stratified Lie groups, extending classical analysis tools to a non-commutative geometric setting.

Contribution

It introduces a new Littlewood-Paley framework for H"older-Zygmund spaces on stratified Lie groups, generalizing existing Euclidean results.

Findings

Established a characterization of $\

on stratified Lie groups.

Extended harmonic analysis techniques to non-commutative settings.

Abstract

In this paper, we give a Littlewood-Paley characterization for the H\"older-Zygmund spaces $\mathcal{C}^{\sigma}(G)$ ($0< \sigma <\infty$) on a stratified Lie group $G$.