Interpolation of sublinear operators on generalized Orlicz and Hardy-Orlicz spaces
William Kraynek (1972)
Studia Mathematica
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William Kraynek (1972)
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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Michał Rzeczkowski (2016)
Annales Polonici Mathematici
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We describe the Banach envelopes of Hardy-Orlicz spaces of analytic functions on an annulus in the complex plane generated by Orlicz functions well-estimated by power-type functions.
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*....
Wojbor A. Woyczyński (1970)
Colloquium Mathematicae
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Pilar Silvestre (2014)
Banach Center Publications
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These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures of the Orlicz function spaces. The goal is to study some aspects of the classical theory of Orlicz spaces for these spaces including the classical theory of interpolation.
Tadeusz Iwaniec, Carlo Sbordone (2004)
Banach Center Publications
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Khalil, Roshdi (1986)
International Journal of Mathematics and Mathematical Sciences
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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.
Juhani Riihentaus, Caiheng Ouyang (1997)
Mathematica Scandinavica
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Lech Maligranda (1989)
Studia Mathematica
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Alberto Torchinsky (1976)
Studia Mathematica
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Elshobaky, E., Faragallah, M. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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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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Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.