Orlicz-Morrey spaces and the Hardy-Littlewood maximal function

• Autorzy: Eiichi Nakai
• Języki publikacji: EN

Abstrakty

EN

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 ∈ L(log L)(ℝⁿ), 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.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 26A33: Fractional derivatives and integrals
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 188
• Numer: 3
• Strony: 193-221

Daty

wydano

2008

Twórcy

autor

Eiichi Nakai

• Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan

Identyfikatory

DOI

10.4064/sm188-3-1