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arXiv · 1302.3436

Some new iterated hardy-type inequalities: The case $\theta = 1$

Amiran Gogatishvili·Rza Chingiz Mustafayev·Lars-Erik Persson
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Abstract

In this paper we characterize the validity of the Hardy-type inequality \begin{equation*} \left\|\left\|\int_s^{\infty}h(z)dz\right\|_{p,u,(0,t)}\right\|_{q,w,\infty}\leq c \,\|h\|_{1,v,\infty} \end{equation*} where $0<p< \infty$, $0<q\leq +\infty$, $u$, $w$ and $v$ are weight functions on $(0,\infty)$. It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces for Hardy-type operators restricted to the cone of monotone functions and for the generalized Stieltjes operator.

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Amiran Gogatishvili, Rza Chingiz Mustafayev, Lars-Erik Persson. 2013-02-14. Some new iterated hardy-type inequalities: The case $\theta = 1$. https://arxiv.org/abs/1302.3436

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