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Landau-type theorem for variable Lebesgue spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe, using elementary methods, the Köthe dual of variable Lebesgue spaces Lp(⋅), called also Nakano spaces, independenly for p(⋅)∈(1,∞) and p(⋅)∈(0,1). The case when p(⋅)∈[1,∞] is also included.
Rocznik
Strony
119--126
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of Engineering Sciences and mathematics, Luleà University of Technology, SE-97187 Luleà, Sweden
autor
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61--614 Poznań, Poland
Bibliografia
  • [1]. A. Alexiewicz, Functional Analysis, Monografie Mat., vol. 49, PWN, Warszawa 1969; in Polish.
  • [2]. C. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs, vol. 105, American Mathematical Society, Providence 2003.
  • [3]. N. K. Bary, A Treatise on Trigonometric Series, Vol. I, II, Pergamon Press, New York 1964.
  • [4]. J. Berger and D. Bridges, A constructive study of Landau’s summability theorem, J. UCS 16 (2010), no. 18, 2523-2534, DOI 10.3217/jucs-016-18-2523.
  • [5]. Z. W. Birnbaum and W. Orlicz, Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen, Studia Math. 3 (1931), 1-67; reprinted in Władysław Orlicz. Collected Papers, PWN, Warszawa 1988, 133-199.
  • [6]. D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces. Foundations and Harmonie Analysis, Birkhäuser, Basel 2013.
  • [7]. L. Diening, P. Harjulehto, P. Hästö, and M. Rużićka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math., vol. 2017, Springer 2011.
  • [8]. G. H. Hardy, J. E. Littlewood, and G. Pölya, Inequalities, Cambridge Univ. Press 1988.
  • [9]. G. Helmberg, A construction concerning (l[exp]p)' ⊂l[exp]q, Amer. Math. Monthly 111 (2004), no. 6, 518-520, DOI 10.2307/4145070.
  • [10]. G. Helmberg, A Landau-type construction concerning (L[exp]p)' ⊂ L[exp]q, Indag. Math. (N.S.) 17 (2006), no. 2, 243-249, DOI 10.1016/S0019-3577(06)80019-4.
  • [11]. H. Hudzik and L. Maligranda, Amemiya norm equals Orlicz norm in general, Indag. Math. (N.S.) 11 (2000), no. 4, 573-585, DOI 10.1016/s0019-3577(00)80026-9.
  • [12]. S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Monogr. Mat., vol. 6, Warsaw 1935.
  • [13]. A. Kamińska and D. Kubiak, The Daugavet property in the Musielak-Orlicz spaces, J. Math. Anal. Appl. 427 (2015), no. 2, 873-898, DOI 10.1016/j.jmaa.2015.02.035.
  • [14]. O. Koväcik and J. Räkosnik, On spaces L[exp](px) and W[exp]k,p(x), Czechoslovak Math. J. 41 (1991), no. 4,592-618.
  • [15]. E. Landau, Über einen Konvergensatz, Göttingen Nachrichten 8 (1907), 25-27.
  • [16]. L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Math., vol. 5, Univ. of Campinas, Campinas 1989.
  • [17]. L. Maligranda, Hidegoro Nakano (1909-1974) - on the centenary of his birth, Proc. of the Third Internat. Symp. on Banach and Function Spaces (ISBFS2009) (Kitakyushu, Japan, 14), Banach and Function Spaces III (M. Kato, L. Maligranda, and T. Suzuki, eds.), Yokohama Publishers, 2011,99-171.
  • [18]. L. Maligranda and L. E. Persson, Generalized duality of some Banach function spaces, Indag. Math. 51 (1989), no. 3, 323-338, DOI 10.1016/S1385-7258(89)80007-l.
  • [19]. L. Maligranda and W. Wnuk, Landau type theorem for Orlicz spaces, Math. Z. 208 (1991), 57-64, DOI 10.1016/sl385-7258(89)80007-l.
  • [20]. J. Musielak, An Introduction to Functional Analysis, PWN, Warszawa 1976; in Polish.
  • [21]. J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, Springer-Verlag, Berlin 1983.
  • [22]. H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen, Tokyo 1950.
  • [23]. H. Nakano, Topology of Linear Topological Spaces, Maruzen, Tokyo 1951.
  • [24]. W. Orlicz, Über konjugierte Exponentenfolgen, Studia Math. 3 (1931), 200-211; reprinted in Władysław Orlicz, Collected Papers, PWN, Warszawa 1988, 200-211.
  • [25]. S.G. Samko, Differentiation and integration of variable order and the space L[exp]p(x) Operator Theory for Complex and Hypercomplex Analysis (Mexico City, 1994), Contemp. Math., vol. 212, American Mathematical Sociaty, Providence, 1998, 203-219, DOI 10.1090/conm/212/02884.
  • [26]. I. I. Sharapudinov, The topology of the space L[exp]p(t) ([0,1]), Mat. Zametki26 (1979), no. 4,613-632; English translation: Math. Notes 26 (1979), no. 3-4,796-806 (1980).
  • [27]. S. Simons, The sequence spaces l(p[sub]v) and m(p[sub]v), Proc. London Math. Soc. (3) 15 (1965), 422-436, DOI 10.1112/plms/s3-15.1.422.
  • [28]. A. Zaanen, Riesz Spaces II, North-Holland, New York Oxford 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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