  For a function $f$ from the Sobolev space $W^{1,p}(C)$
($C\subset\mathbb{R}^d$ is an open convex cone), a sharp inequality that
estimates $\| f\|_{L_{\infty}}$ via the $L_{p}$-norm of its gradient and a
seminorm of the function is obtained. With the help of this inequality, a sharp
inequality is proved, which estimates the ${L_{\infty}}$-norm of the
Radon--Nikodym derivative of a charge defined on Lebesgue measurable subsets of
$C$ via the $L_p$-norm of the gradient of this derivative and a seminorm of the
charge. In the case, when $C=\mathbb{R}_+^m\times \mathbb{R}^{d-m}$, $0\le m\le
d$, we obtain inequalities that estimate the ${L_{\infty}}$-norm of a mixed
derivative of a function $f\colon C\to \mathbb{R}$ using its
${L_{\infty}}$-norm and the $L_p$-norm of the gradient of the function's mixed
derivative.
