Exact estimates of functions in Sobolev spaces with uniform norm

For functions from the Sobolev space ${\stackrel{°}{W}}_{\infty }^n[0;1]$ and an arbitrary point $a\in (0;1)$, the best estimates are obtained in the inequality $\left|f\left(a\right)\right|\le A_{n\mathrm{,0,}\infty }\left(a\right)\cdot ||f^n||L_{\infty }\left[041\right]$. The connection of these estimates with the best approximations of splines of a special kind by polynomials in $L_1\left[0;1\right]$ and with the Peano kernel is established. Exact constants of embedding the space ${\stackrel{°}{W}}_{\infty }^n[0;1]$ in $L_{{}_{}^{\infty }}\left[0;1\right]$ are found.