Estimates for n-widths of the Hardy-type operators (Addendum to "Improved estimates for the approximation numbers of the Hardy-type operators")

Consider the Hardy-type operator T: L-p (a, b) --> L-p (a, b), -infinity <= a< b <= infinity, which is defined by (Tf)(x) = v(x) integral(x)(a) u(t) f (t) dt. It is shown that rho(n) (T) = 1/n alpha(p) integral(b)(a) u(x)v(x) + O(n(-2)), where rho(n) (T) stands for any of the following: the Kolmogorov n-width, the Gel'fand n-width, the Bernstein n-width or the nth approximation number of T. (C) 2006 Elsevier Inc. All rights reserved.