Weighted iterated Hardy-type inequalities
Classical Analysis and ODEs
2015-03-16 v1 Analysis of PDEs
Functional Analysis
Abstract
In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing functions to the cone of non-increasing functions and vice versa not changing the operator . New characterizations of the weighted Hardy-type inequalities on the cones of monotone functions are given. The validity of so-called weighted iterated Hardy-type inequalities are characterized.
Cite
@article{arxiv.1503.04079,
title = {Weighted iterated Hardy-type inequalities},
author = {Amiran Gogatishvili and Rza Mustafayev},
journal= {arXiv preprint arXiv:1503.04079},
year = {2015}
}