On linear functionals in Hardy-Orlicz spaces, I
R. Leśniewicz (1973)
Studia Mathematica
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R. Leśniewicz (1973)
Studia Mathematica
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Yuzan He (1988)
Annales Polonici Mathematici
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Wojbor A. Woyczyński (1970)
Colloquium Mathematicae
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Khalil, Roshdi (1986)
International Journal of Mathematics and Mathematical Sciences
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Tadeusz Iwaniec, Carlo Sbordone (2004)
Banach Center Publications
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Eiichi Nakai (2008)
Studia Mathematica
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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.
Andreas Hartmann (1999)
Studia Mathematica
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William Kraynek (1972)
Studia Mathematica
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Juhani Riihentaus, Caiheng Ouyang (1997)
Mathematica Scandinavica
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Diego Gallardo (1988)
Publicacions Matemàtiques
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Let M be the Hardy-Littlewood maximal operator defined by: Mf(x) = supx ∈ Q 1/|Q| ∫Q |f| dx, (f ∈ Lloc(Rn)), where the supreme is taken over all cubes Q containing x and |Q| is the Lebesgue measure of Q. In this paper we characterize the Orlicz spaces Lφ*, associated to N-functions φ, such that M is bounded in Lφ*....
Lech Maligranda, Katsuo Matsuoka (2015)
Colloquium Mathematicae
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We define Beurling-Orlicz spaces, weak Beurling-Orlicz spaces, Herz-Orlicz spaces, weak Herz-Orlicz spaces, central Morrey-Orlicz spaces and weak central Morrey-Orlicz spaces. Moreover, the strong-type and weak-type estimates of the Hardy-Littlewood maximal function on these spaces are investigated.
E.R. Love (1986)
Mathematische Zeitschrift
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N. J. Kalton (2004)
Banach Center Publications
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We survey some questions on Rademacher series in both Banach and quasi-Banach spaces which have been the subject of extensive research from the time of Orlicz to the present day.
Fon-Che Liu (2008)
Studia Mathematica
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A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.
Tao Zhang (2003)
Annales Polonici Mathematici
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Estimation of the Jung constants of Orlicz sequence spaces equipped with either the Luxemburg norm or the Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz sequence spaces are found by using new quantitative indices for 𝓝-functions.
Ha Huy Bang, Nguyen Van Hoang, Vu Nhat Huy (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate best constants for inequalities between the Orlicz norm and Luxemburg norm in Orlicz spaces.
Hudzik, Henryk
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Paweł Kolwicz (2005)
Banach Center Publications
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We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
Michał Kisielewicz (1975)
Annales Polonici Mathematici
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Lech Maligranda, Witold Wnuk (2004)
Banach Center Publications
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Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza (2008)
Colloquium Mathematicae
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We give new proofs that some Banach spaces have Pełczyński's property (V).
Jimin Zheng, Lihuan Sun, Yun'an Cui (2008)
Banach Center Publications
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In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.