An extension of Hedberg's convolution inequality and applications
type: Item
instance of: scholarly article
title: An extension of Hedberg's convolution inequality and applications
zbMATH Open document ID: 0914.42014
author: Andrea Cianchi
author: Bianca Stroffolini
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-27T00:00:00Z
review text: In his celebrated paper [Proc. Am. Math. Soc. 36, 505-510 (1993; Zbl 0283.26003)], \textit{L. I. Hedberg} presented a new proof of the Sobolev inequality for potentials, which asserts, roughly speaking, that the Riesz potential of order \(\alpha\in(0,n)\) is bounded from \(L^p(\mathbb R^n)\) into \(L^q(\mathbb R^n)\) when \(p\in(1,n/\alpha)\) and \(q=np/(n-\alpha p)\). Hedberg's method is based on a pointwise inequality linking together the Riesz potential and the Hardy-Littlewood maximal operator. The paper under review presents an Orlicz-space version of Hedberg's pointwise inequality and its very interesting applications. In particular, sharp embeddings of Orlicz-Sobolev spaces into Orlicz spaces are obtained. Examples including the limiting case \(p=n/\alpha\) are discussed.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1236168
zbMATH Keywords: Riesz potential
zbMATH Keywords: maximal operator
zbMATH Keywords: Hedberg's convolution inequality
zbMATH Keywords: Orlicz spaces
reviewed by: Luboš Pick
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6092
OpenAlex ID: W2072682284
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DOI: 10.1006/JMAA.1998.6092
description: scientific article; zbMATH DE number 1236168