An intersection representation for a class of anisotropic vector-valued function spaces

Abstract

The main result of this paper is an intersection representation for a class of anisotropic vector-valued function spaces in an axiomatic setting \\`a la Hedberg$\\&$Netrusov, which includes weighted anisotropic mixed-norm Besov and Triebel-Lizorkin spaces. In the special case of the classical Triebel-Lizorkin spaces, the intersection representation gives an improvement of the well-known Fubini property. The motivation comes from the weighted $L_{q}$-$L_{p}$-maximal regularity problem for parabolic boundary value problems, where weighted anisotropic mixed-norm Triebel-Lizorkin spaces occur as spaces of boundary data.