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We consider the Hardy-type operator (T f) (x) := v(x) x a u(t)f (t)dt, x > a, and establish properties of T as a map from L p (a, b) into L q (a, b) for 1 < p ≤ q ≤ 2, 2 ≤ p ≤ q < ∞ and 1 < p ≤ 2 ≤ q < ∞. The main result is that, with appropriate assumptions on u and v, the approximation numbers a n (T) of T satisfy the inequality c 1 b a |uv| r dt ≤ lim(More)
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