Maximal functions in variable exponent spaces: limiting cases of the exponent

Lars Diening, Petteri Harjulehto, Peter Hästö, Yoshihiro Mizuta, Tetsu Shimomura

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"In this paper we study the Hardy-Littlewood maximal operator in variable exponent spaces when the exponent is not assumed to be bounded away from 1 aud infinity. Within the framework of Orlicz-Musielak spaces, we characterize the function space X with the property that M f is an element of L-p(.) if and only if f is an element of X, under the assumptions that p is log-Holder continuous aud 1 <= p(-) <= p(+) <=infinity."
Original languageEnglish
JournalAnnales Academiae Scientiarum Fennicae. Mathematica
Issue number2
Pages (from-to)503-522
Number of pages20
Publication statusPublished - 2009
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

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