Approximation numbers and Kolmogorov widths of Hardy‐type operators in a non‐homogeneous case

Let I = a , b ] ? ?, let 1 < q ≤ p < ∞, let u and v be positive functions with u ∈ L _{p ′} (I ) and v ∈ L _q (I ), and let T : L _p (I ) → L _q (I ) be the Hardy‐type operator given by Given any n ∈ ?, let s _n stand for either the n ‐th approximation number of T or the n ‐th Kolmogorov width of T . We show that where c _pq is an explicit constant depending only on p and q . (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)