Integral inequalities and equalities for the rearrangement of Hardy and Littlewood
type: Item
instance of: scholarly article
title: Integral inequalities and equalities for the rearrangement of Hardy and Littlewood
zbMATH Open document ID: 0815.26009
author: Alexander Stanoyevitch
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-07-05T00:00:00Z
review text: Suppose \(f: [0, 1]\to \mathbb{R}\) is differentiable a.e., \(\Phi: \mathbb{R}\to [0, \infty)\) is Borel measurable, and that \(\Psi: [0, \infty)\to \mathbb{R}\) is increasing. Let \(f^*\) stand for non-increasing rearrangement of \(f\). The author proves that \[ \int^ 1_ 0 \Phi(f^* (x)) \Psi(| (f^*)'|) dx\leq \int^ 1_ 0 \Phi(f(x)) \Psi(| f'(x)|) dx\leqno{(*)} \] and, under some additional assumptions on \(f\), \(\Phi\), and \(\Psi\), he investigates the case of equality in \((*)\).
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 599911
zbMATH Keywords: integral inequality
zbMATH Keywords: non-increasing rearrangement
reviewed by: Bohumír Opic
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1157
OpenAlex ID: W2020627373
DOI: 10.1006/JMAA.1994.1157
Recommended article: Q3349113
Recommended article: Integral inequalities related to Hardy's inequality
Recommended article: On a class of integral inequalities of Hardy-Littlewood type
Recommended article: On some inequalities related to Hardy's integral inequality
Recommended article: Q5315966
Recommended article: On some integral inequalities similar to Hardy's inequality
Recommended article: Rearrangement inequality for the Hardy-Littlewood maximal operator
Recommended article: On An Inequality of Hardy and Littlewood
Recommended article: Some inequalities of Hardy-Littlewood type
Recommended article: A general rearrangement inequality à la Hardy-Littlewood
description: scientific article; zbMATH DE number 599911