Some new iterated hardy-type inequalities: The case $\theta = 1$
Classical Analysis and ODEs
2013-02-15 v1 Analysis of PDEs
Functional Analysis
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 , , , and are weight functions on . 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.
Keywords
Cite
@article{arxiv.1302.3436,
title = {Some new iterated hardy-type inequalities: The case $\theta = 1$},
author = {Amiran Gogatishvili and Rza Chingiz Mustafayev and Lars-Erik Persson},
journal= {arXiv preprint arXiv:1302.3436},
year = {2013}
}