Trace and extension operators for Besov spaces and Triebel-Lizorkin spaces with variable exponents

TL;DR

This paper investigates the boundedness of trace and extension operators for Besov and Triebel-Lizorkin spaces with variable exponents on upper half spaces, introducing a quarkonial decomposition for these spaces.

Contribution

It introduces a quarkonial decomposition for variable exponent Besov and Triebel-Lizorkin spaces and studies the boundedness of trace and extension operators on upper half spaces.

Findings

Established boundedness of trace operators.

Developed a quarkonial decomposition for variable exponent spaces.

Analyzed extension operators on upper half spaces.

Abstract

This paper is concerned with a boundedness of trace and extension operators for Besov spaces and Triebel-Lizorkin spaces on upper half space with variable exponents. To define trace and extension operators, we introduce a quarkonial decomposition for Besov spaces and Triebel-Lizorkin spaces with variable exponents on ${\mathbb R}^n$. Furthermore, we study trace and extension operators for Besov spaces and Triebel-Lizorkin spaces with variable exponents on upper half spaces ${\mathbb R}^n_+$.