The Hardy-Littlewood maximal function of a Sobolev function
type: Item
instance of: scholarly article
title: The Hardy-Littlewood maximal function of a Sobolev function
zbMATH Open document ID: 0882.43003
DOI: 10.1007/BF02773636
author: Juha Kinnunen
published in: Israel Journal of Mathematics
publication date: 1997-09-17T00:00:00Z
review text: In this paper a main result is that the Hardy-Littlewood maximal operator is bounded in the Sobolev space \(W^{1,p}(\mathbb{R}^n)\) for \(1<p\leq\infty\). This result is applied to study a weak type inequality for the Sobolev capacity and to prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1062358
zbMATH Keywords: quasi-continuity
zbMATH Keywords: Hardy-Littlewood maximal operator
zbMATH Keywords: Sobolev space
zbMATH Keywords: Sobolev capacity
zbMATH Keywords: Hardy-Littlewood maximal function
reviewed by: Koichi Saka
MaRDI profile type: Publication
cites work: Q4321362
cites work: Q5648620
cites work: Q5187597
cites work: On very weak solutions of certain elliptic systems
cites work: Q5607484
full work available at URL: https://doi.org/10.1007/bf02773636
OpenAlex ID: W2091683986
description: scientific article; zbMATH DE number 1062358