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

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 ${\mathbb{R}}_{+}^n$.