# Besov and Triebel--Lizorkin spaces on Lie groups

## TL;DR

This paper develops a comprehensive theory of Besov and Triebel--Lizorkin spaces on noncompact Lie groups with sub-Riemannian structures, using hypoelliptic sub-Laplacians and characterizing their properties.

## Contribution

It introduces new definitions and characterizations of these function spaces on Lie groups, extending classical analysis to more general geometric settings.

## Key findings

- Established equivalent norm characterizations
- Compared these spaces with Sobolev spaces
- Analyzed their interpolation and algebra properties

## Abstract

In this paper we develop a theory of Besov and Triebel--Lizorkin spaces on general noncompact Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means of hypoelliptic sub-Laplacians with drift, and endowed with a measure whose density with respect to a right Haar measure is a continuous positive character of the group. We prove several equivalent characterizations of their norms, we establish comparison results also involving Sobolev spaces of recent introduction, and investigate their complex interpolation and algebra properties.