The Hardy-Littlewood maximal function of a Sobolev function

Juha Kinnunen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

111 Citations (Scopus)

Abstract

We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev space W1,p(Rn) for 1 <p ≤ ∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.

Original languageEnglish
Pages (from-to)117-124
Number of pages8
JournalIsrael Journal of Mathematics
Volume100
Issue number1
DOIs
Publication statusPublished - Dec 1997
MoE publication typeA1 Journal article-refereed

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