An Intersection Representation for a Class of Anisotropic Vector-valued Function Spaces

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$\mathrm{\&}$Netrusov, which includes weighted anisotropic mixed-norm Besov and Lizorkin-Triebel spaces. In the special case of the classical Lizorkin-Triebel spaces, the intersection representation gives an improvement of the well-known Fubini property. The main result has applications in the weighted $L_q$-$L_p$-maximal regularity problem for parabolic boundary value problems, where weighted anisotropic mixed-norm Lizorkin-Triebel spaces occur as spaces of boundary data.