Exact estimates of functions in Sobolev spaces with uniform norm

For functions from the Sobolev spaceW°∞n[0;1]and an arbitrary pointa∈(0;1), the best estimates are obtained in the inequalityf(a)≤An,0,∞(a)⋅fnL∞[041]. The connection of these estimates with the best approximations of splines of a special kind by polynomials inL10;1and with the Peano kernel is established. Exact constants of embedding the spaceW°∞n[0;1]inL∞0;1are found.