✦ LIBER ✦
Approximation numbers and Kolmogorov widths of Hardy-type operators in a non-homogeneous case
✍ Scribed by D. E. Edmunds; J. Lang
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 203 KB
- Volume
- 279
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let 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)