The derivative of the maximal function

Juha Kinnunen*, Peter Lindqvist

*Corresponding author for this work

Research output: Contribution to journalArticle

65 Citations (Scopus)

Abstract

In this note we show that the local Hardy-Littlewood maximal operator is bounded in the Sobolev space. Thus the maximal function often has partial derivatives. We also show that the maximal operator preserves the zero boundary values in Sobolev's sense.

Original languageEnglish
Pages (from-to)161-167
Number of pages7
JournalJOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume503
Publication statusPublished - 1998
MoE publication typeA1 Journal article-refereed

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