**
J. Rákosník (ed.), **

Function spaces, differential operators and nonlinear analysis.

Proceedings of the conference held in Paseky na Jizerou, September 3-9, 1995.

Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha 1996

p. 215 - 220

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On the approximation numbers of Hardy-type operators

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Desmond J. Harris

Pryske Cottage, Llanishen, Chepstow, Gwent NP6 6QD, United Kingdom w.d.evans@cardiff.ac.uk

**Abstract:** Under certain conditions, asymptotic bounds are obtained for the approximation numbers of the weighted Hardy-type operator $$ Tf(x) = v(x)\int_0^xf(t)u(t)dt,\quad L^p(0,\infty) \rightarrow L^p(0,\infty),\quad 1<p<\infty, $$ where $u \in L^{p^{\prime}}_{\text {loc}}(0,\infty)$, $v\in L^p(0,\infty)$ and $u^{p^{\prime}}/v^p$ is non-decreasing. If $p=2$, the bounds give an asymptotic formula.

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