Weighted inequalities for the fractional integral operators on monotone functions
type: Item
instance of: scholarly article
title: Weighted inequalities for the fractional integral operators on monotone functions
zbMATH Open document ID: 0840.42012
DOI: 10.4171/ZAA/689
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-03-17T00:00:00Z
review text: Summary: We give a characterization of weight functions \(u\) and \(v\) on \(\mathbb{R}^n\) for which the fractional integral operator \(I_s\) of order \(s\) on \(\mathbb{R}^n\) defined by \((I_s f)(x)= \int_{\mathbb{R}^n} |x- y|^{s-n} f(y)dy\) sends all monotone functions which belong to the weighted Lebesgue space \(L^p_v(\mathbb{R}^n)\) into the weighted Lebesgue space \(L^q_u(\mathbb{R}^n)\). This characterization is done for all \(p\) and \(q\) with \(1< p< \infty\) and \(0< q< \infty\). The analogous Lorentz and Orlicz problems are also considered.
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 856807
zbMATH Keywords: weighted inequalities
zbMATH Keywords: Hardy operators
zbMATH Keywords: fractional integral operator
author: Yves Rakotondratsimba
MaRDI profile type: Publication
cites work: Weighted $L_{Φ}$ integral inequalities for operators of Hardy type
cites work: Q4325008
cites work: Weighted Hardy Inequalities for Increasing Functions
cites work: Q4002299
cites work: Weighted Inequalities for Geometric Means
cites work: Two Weight Φ-Inequalities for the Hardy Operator, Hardy-Littlewood Maximal Operator, and Fractional Integrals
cites work: Boundedness of classical operators on classical Lorentz spaces
cites work: Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces
cites work: The Weighted Hardy's Inequality for Nonincreasing Functions
cites work: Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators
full work available at URL: https://doi.org/10.4171/zaa/689
OpenAlex ID: W2050428742
description: scientific article; zbMATH DE number 856807