  Under some assumptions on the vectors $a_{1},..,a_{n} \in\mathbb{R}^{k}$ and
the function $B : \mathbb{R}^{n} \to \mathbb{R}$ we find the sharp estimate of
the expression $\int_{\mathbb{R}^{k}} B(u_{1}(a_{1}\cdot x),...,
u_{n}(a_{n}\cdot x))dx$ in terms of $\int_{\mathbb{R}}u_{j}(y)dy, j=1,...,n.$
In some particular case we will show that these assumptions on $B$ imply that
there is only one Brascamp--Lieb inequality.

Analysis of PDEs;Classical Analysis and ODEs