Lipschitz space with mixed logarithmic smoothness and embedding theorems

TL;DR

This paper studies a specific Lipschitz space characterized by mixed logarithmic smoothness for periodic functions of multiple variables, providing new norm descriptions and embedding relations with Besov spaces.

Contribution

It introduces equivalent norm descriptions for the Lipschitz space with mixed logarithmic smoothness and establishes embedding theorems with Besov spaces.

Findings

Equivalent norm descriptions of the Lipschitz space

Embedding theorems between Besov and Lipschitz spaces

Enhanced understanding of function space relationships

Abstract

This article considers the Lipschitz space with mixed logarithmic smoothness of $2\pi$ periodic functions of several variables. We obtain equivalent descriptions of the norm of the Lipschitz space and prove embedding theorems between Besov and Lipschitz spaces.