On boundedness of maximal functions in Sobolev spaces

Piotr Hajłasz, Jani Onninen

Research output: Contribution to journalArticle

67 Scopus citations

Abstract

Kinnunen and Lindqvist proved in [9] that the local Hardy-Littlewood maximal function, defined in an open set Ω in the Euclidean space, is a bounded operator from W1,p(Ω) to W1,p (Ω), provided p > 1. In this note we give a simpler argument which leads to a slightly more general result. Furthermore, the argument also allows us to prove boundedness of the spherical maximal function in the Sobolev space W 1,p(Ω), p > n/(n - 1). We also raise many questions concerning boundedness of maximal operators in Sobolev spaces.

Original languageEnglish (US)
Pages (from-to)167-176
Number of pages10
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume29
Issue number1
StatePublished - May 10 2004
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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