Besov spaces generated by the Neumann Laplacian

TL;DR

This paper defines Besov spaces associated with the Neumann Laplacian, explores their fundamental properties, and establishes a fractional Leibniz rule within these spaces, advancing the mathematical understanding of these function spaces.

Contribution

It introduces a new class of Besov spaces generated by the Neumann Laplacian and proves their fundamental properties, including a fractional Leibniz rule, which was not previously established.

Findings

Defined Besov spaces via the Neumann Laplacian

Proved fundamental properties of these spaces

Established a fractional Leibniz rule in these Besov spaces

Abstract

The purpose of this paper is to give a definition and prove the fundamental properties of Besov spaces generated by the Neumann Laplacian. As a by-product of these results, the fractional Leibniz rule in these Besov spaces is obtained.