, Volume 22, Issue 1, pp 275–299 | Cite as

On weighted iterated Hardy-type inequalities



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 \((0,\infty )\).


Quasilinear operators Iterated Hardy inequalities Weights 

Mathematics Subject Classification

26D10 26D15 



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


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsAcademy of Sciences of AzerbaijanBakuAzerbaijan

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