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.

本文的主要结果是在公理化的环境中，一类各向异性矢量值函数空间的交集表示，如Hedberg和Netrusov（2007），其中包括加权各向异性混合范数Besov和Lizorkin-Triebel空间。在经典的Lizorkin-Triebel空间的特殊情况下，交点表示法改善了众所周知的Fubini属性。主要结果在加权中有应用${\mathrm{大号}}_q$--${\mathrm{大号}}_p$-抛物型边值问题的最大正则性问题，其中加权各向异性混合范数Lizorkin-Triebel空间作为边界数据空间出现。