Weighted Young inequalities for convolutions
type: Item
instance of: scholarly article
title: Weighted Young inequalities for convolutions
zbMATH Open document ID: 1034.42019
published in: Southeast Asian Bulletin of Mathematics
publication date: 2003-03-18T00:00:00Z
review text: Let \(1 < p, q < \infty\) and let \(u\) and \(v\) be weighted functions on \(\mathbb R^n\). The aim of the paper is to find sufficient conditions for the validity of the inequality \[ \Bigl(\int_{\mathbb R^n} (g \times f)^q (x)\, u (x) \, dx\Bigr)^{1/q} \leq C \| g\| _X \Bigl(\int_{\mathbb R^n} f (x)^p \, v (x) \, dx\Bigr)^{1/p} \] for all measurable and non-negative functions \(f, g\) on \(\mathbb R^n\) with \(g\) radial and satisfying a convenient growth condition. Here \(X\) is a Banach function space and \(C\) is a~ positive constant.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 1884054
zbMATH Keywords: weighted inequalities
zbMATH Keywords: convolutions
zbMATH Keywords: \(n\)-dimensional Hardy's inequality
author: Yves Rakotondratsimba
reviewed by: Bohumír Opic
MaRDI profile type: Publication
full work available at URL: s100120200030
OpenAlex ID: W1978831201
DOI: 10.1007/S100120200030
description: scientific article; zbMATH DE number 1884054