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

Abstract

AbstractLet I = [a , b ] ⊂ ℝ, 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 equation image Given any n ∈ 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 equation image where c pq is an explicit constant depending only on p and q . (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)