Ales Nekvinda

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We consider the Hardy-type operator (Tf) (x) := v(x) ∫ x a u(t)f(t)dt, x > a, and establish properties of T as a map from L(a, b) into L(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 an(T ) of T satisfy the inequality c1 ∫ b a |uv|dt ≤ lim inf n→∞(More)
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