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On weighted iterated Hardy-type inequalities

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Abstract

In this paper the inequality

$$\begin{aligned} \bigg ( \int _0^{\infty } \bigg ( \int _x^{\infty } \bigg ( \int _t^{\infty } h \bigg )^q w(t)\,dt \bigg )^{r / q} u(x)\,{ ds} \bigg )^{1/r}\le C \,\int _0^{\infty } h v, \quad h \in {\mathfrak {M}}^+(0,\infty ) \end{aligned}$$

is characterized. Here \(0< q ,\, r < \infty \) and \(u,\,v,\,w\) are weight functions on \((0,\infty )\).

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Notes

  1. For any \(a\in \mathbb {R}\) denote by \(a_+ = a\) when \(a>0\) and \(a_+ = 0\) when \(a \le 0\).

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Acknowledgements

We thank the anonymous referee for his/her remarks, which have improved the final version of this paper.

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  1. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, B. Vahabzade St. 9, AZ 1141, Baku, Azerbaijan

    Rza Mustafayev

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  1. Rza Mustafayev
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Mustafayev, R. On weighted iterated Hardy-type inequalities. Positivity 22, 275–299 (2018). https://doi.org/10.1007/s11117-017-0512-y

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