Nikolskii inequality and functional classes on compact Lie groups

TL;DR

This paper investigates various function spaces on compact Lie groups, emphasizing the role of the Nikolskii inequality in their analysis, contributing to harmonic analysis and functional analysis on these groups.

Contribution

It introduces new insights into the interplay between Nikolskii inequality and function spaces like Besov, Triebel-Lizorkin, Wiener, and Beurling on compact Lie groups.

Findings

Establishment of inequalities relating function space norms

Characterization of function spaces using Nikolskii inequality

Applications to harmonic analysis on compact Lie groups

Abstract

In this note we study Besov, Triebel-Lizorkin, Wiener, and Beurling function spaces on compact Lie groups. A major role in the analysis is played by the Nikolskii inequality.