On the approximation numbers of Hardy-type operators

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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