On the best approximation by ridge functions in the uniform norm

We consider the best approximation of some function classes by the manifold M-n consisting of sums of n arbitrary ridge functions. It is proved that t he deviation of the Sobolev class W-p(r,d) from the manifold M-n in the spa ce L-q for any 2 less than or equal to q less than or equal to p less than or equal to infinity behaves asymptotically as n(-r/(d-1)). In particular, we obtain this asymptotic estimate for the uniform norm p = q = infinity.