## Y. Benoist and T. Kobayashi. Tempered homogeneous spaces IV. preprint. 33 pages.

Let $G$ be a complex semisimple Lie group and $H$ a complex closed connected subgroup. Let $\mathfrak{g}$ and $\mathfrak{h}$ be their Lie algebras. We prove that the regular representation of $G$ in $L^2(G/H)$ is tempered if and only if the orthogonal of $\mathfrak{h}$ in $\mathfrak{g}$ contains regular elements.