Orlicz–Morrey spaces and the Hardy–Littlewood maximal function

Volume 188 / 2008

Eiichi Nakai Studia Mathematica 188 (2008), 193-221 MSC: 46E30, 42B35, 42B25, 26A33. DOI: 10.4064/sm188-3-1

Abstract

We prove basic properties of Orlicz–Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy–Littlewood maximal operator $M$ from one Orlicz–Morrey space to another. For example, if $f\in L(\log L)(\mathbb R^n)$, then $Mf$ is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of $M$, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.

Authors

  • Eiichi NakaiDepartment of Mathematics
    Osaka Kyoiku University
    Kashiwara, Osaka 582-8582, Japan
    e-mail

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