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On submultiplicativity of an N-function and its conjugate
- 作者:Lech Maligranda
- 关键词:46E30 ; 46B20 ; 46B42 ; Orlicz functions ; submultiplicative functions ; power function
- 刊名:Aequationes Mathematicae
- 出版年:2015
- 出版时间:June 2015
- 年:2015
- 卷:89
- 期:3
- 页码:569-573
- 全文大小:408 KB
- 参考文献:1.Finol C.E., Maligranda L.: On a decomposition of some functions. Comment. Math. Prace Mat. 30(2), 285-91 (1991)MATH MathSciNet
2.Finol C.E., Wójtowicz M.: Multiplicative properties of real functions with applications to classical functions. Aequationes Math. 59(1-2), 134-49 (2000)View Article MATH MathSciNet 3.Garrigós G., Hernández E., Martell J.M.: Wavelets, Orlicz spaces, and greedy bases. Appl. Comput. Harmon. Anal. 24(1), 70-3 (2008)View Article MATH MathSciNet 4.Gustavsson J., Maligranda L., Peetre J.: A submultiplicative function. Indag. Math. 51, 435-42 (1989)View Article MATH MathSciNet 5.Hudzik H., Maligranda L.: Some remarks on subultiplicative Orlicz functions. Indag. Math. (N.S.) 3(3), 313-21 (1992)View Article MATH MathSciNet 6.Hudzik H., Maligranda L., Masty?o M., Persson L.E.: Extension of submultiplicativity and supermultiplicativity of Orlicz functions. Real Anal. Exchange 24(2), 567-78 (1998/99)MATH 7.Krasnoselskii M.A., Rutickii Ya.B.: Convex Functions and Orlicz Spaces. Noordhoff Ltd., Groningen (1961) 8.Krni? M.: Multidimensional Hilbert-type inequality on the weighted Orlicz spaces. Mediterr. J. Math. 9(4), 883-95 (2012)View Article MATH MathSciNet 9.Krni?, M., Pe?ari?, J., Peri?, I., Vukovi?, P.: Recent Advances in Hilbert-Type Inequalities, Monographs in Inequalities 3, Element, Zagreb (2012) 10.Krugljak N., Maligranda L.: Calderón-Lozanovski? construction on weighted Banach function lattices. J. Math. Anal. Appl. 288(2), 744-57 (2003)View Article MATH MathSciNet 11.Kuang J.C., Debnath L.: On Hilbert’s type inequalities on the weighted Orlicz spaces. Pac. J. Appl. Math. 1, 89-7 (2008)MathSciNet 12.Lindenstrauss J., Tzafriri L.: Classical Banach Spaces, I. Sequence Spaces. Springer, Berlin (1977)View Article MATH 13.Maligranda, L.: Indices and Interpolation, Dissertationes Math. (Rozprawy Mat.) 234, 1-2 (1985) 14.Maligranda, L. Orlicz Spaces and Interpolation. Seminars in Mathematics, vol. 5. Univ. Estadual de Campinas, Campinas SP, Brazil (1989) 15.Maligranda L.: Calderón-Lozanovski? construction for mixed norm spaces. Acta Math. Hungar. 103(4), 279-02 (2004)View Article MATH MathSciNet 16.Maligranda, L.: Review of the paper [8]. Math. Rev. MR2991170, June (2013) 17.Rao M.M., Ren Z.D.: Theory of Orlicz Spaces. Marcel Dekker, New York (1991)MATH 18.Salekhov, D.V.: On a property of N-functions. Mat. Zametki 3(4), 281-90 (1968); English transl. in: Math. Notes 3(4), 662-67 (1968) 19.Wojtaszczyk, P.: Greediness of the Haar system in rearrangement invariant spaces, vol. 72, pp. 385-95. Banach Center Publications, Warszawa (2006) 20.Zippin M.: On perfectly homogeneous bases in Banach spaces. Israel J. Math. 4, 265-72 (1966)View Article MATH MathSciNet
- 作者单位:Lech Maligranda (1)
1. Department of Engineering Sciences and Mathematics, Lule? University of Technology, 971 87, Lule?, Sweden
- 刊物类别:Mathematics and Statistics
- 刊物主题:Mathematics
Analysis Combinatorics
- 出版者:Birkh盲user Basel
- ISSN:1420-8903
文摘
It is shown that if an N-function φ is submultiplicative, then its conjugate function φ* cannot be submultiplicative. Moreover, we have the following characterization of power functions among N-functions: if an N-function φ is C 1-submultiplicative and its conjugate function φ* is C 2-submultiplicative for some C 1, C 2 >? 0, then φ is equivalent to a power function.
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