Weighted Hardy's inequalities for negative indices
type: Item
instance of: scholarly article
title: Weighted Hardy's inequalities for negative indices
zbMATH Open document ID: 1068.26022
DOI: 10.5565/PUBLMAT_48204_08
published in: Publicacions Matemàtiques
publication date: 2005-03-14T00:00:00Z
full work available at URL: https://eudml.org/doc/41500
review text: The aim of the paper is to characterize the validity of the reverse Hardy inequality \[ \Big(\int^{\infty}_0 f(x)^p \,dx\Big)^{1/p} \leq C \Big(\int^{\infty}_0 u(x) \Big(\int^x_0 f(y)v(y)\,dy\Big)^q\,dx\Big)^{1/q}, \;f \geq 0, \] provided that either \(p,q < 0\) or \(p,q \in (0,1)\). (Here \(u\) and \(v\) are weight functions on \((0,\infty)\) and \(C\) is a positive constant independent of \(f\).) Moreover, the author establishes a duality between these two cases.
reviewed by: Bohumír Opic
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 2145404
zbMATH Keywords: reverse Hardy inequalities
zbMATH Keywords: weight functions
author: Dmitri V. Prokhorov
MaRDI profile type: Publication
OpenAlex ID: W4214620716
description: scientific article; zbMATH DE number 2145404