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 à la Hedberg and Netrusov (2007), 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.