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  • 1 Parthenope University of Naples, , via Generale Parisi 13, Palazzo Pacanowsky, 80132, Napoli, , Italy
  • | 2 Department of Mathematics and Statistics, , Bar-Ilan University, 59200, Ramat Gan, , Israel
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We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces.

We also find the exact value of the embedding constant which appears in the corresponding norm inequality.

  • [1]

    I. Ahmed , A. Fiorenza , M. R. Formica , A. Gogatishvili and J.M. Rakotoson . Some new results related to Lorentz GΓ-spaces and interpolation. J. Math. Anal. Appl., 483(2):24 pp., 2020.

    • Search Google Scholar
    • Export Citation
  • [2]

    I. Ahmed , A. Fiorenza and A. Hafeez . Some Interpolation Formulae for Grand and Small Lorentz Spaces. Mediterr. J. Math., 17(2):Art. 57, 21 pp., 2020.

    • Search Google Scholar
    • Export Citation
  • [3]

    G. Anatriello and M.R. Formica . Weighted fully measurable grand Lebesgue spaces and the maximal theorem. Ric. Mat., 65(1):221233, 2016.

    • Search Google Scholar
    • Export Citation
  • [4]

    G. Anatriello , M. R. Formica and R. Giova . Fully measurable small Lebesgue spaces. J. Math. Anal. Appl., 447(1):550563, 2017.

  • [5]

    T. Andô , On products of Orlicz spaces. Math. Ann., 140:174186, 1960.

  • [6]

    C. Bennett and R. Sharpley . Interpolation of Operators. Academic Press, New York, 1988.

  • [7]

    C. Capone and M. R. Formica . A decomposition of the dual space of some Banach function spaces. J. Funct. Spaces Appl. 2012, Art. ID 737534, 10 pp.

    • Search Google Scholar
    • Export Citation
  • [8]

    C. Capone , M. R. Formica and R. Giova . Grand Lebesgue spaces with respect to measurable functions. Nonlinear Anal., 85:125131, 2013.

    • Search Google Scholar
    • Export Citation
  • [9]

    M. J. Carro , J. Raposo and J. Soria . Recent developments in the theory of Lorentz spaces and weighted inequalities. Mem. Amer. Math. Soc., 187(877):xii+128, 2007.

    • Search Google Scholar
    • Export Citation
  • [10]

    A. Cianchi . Strong and weak type inequalities for some classical operators in Orlicz spaces. J. London Math. Soc.(2), 60(1):187202, 1999.

    • Search Google Scholar
    • Export Citation
  • [11]

    M. Cwikel , A. Kaminska , L. Maligranda and L. Pick . Are generalized Lorentz “spaces” really spaces?. Proc. Amer. Math. Soc., 132(12):36153625, 2004.

    • Search Google Scholar
    • Export Citation
  • [12]

    D. Cruz-Uribe and M. Krbec . Localization and extrapolation in Orlicz-Lorentz spaces. Function spaces, interpolation theory and related topics (Lund, 2000), 273283, de Gruyter, Berlin, 2002.

    • Search Google Scholar
    • Export Citation
  • [13]

    D.E. Edmunds and W.D. Evans . Hardy operators, function spaces and embeddings. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2004.

    • Search Google Scholar
    • Export Citation
  • [14]

    D. E. Edmunds and M. Krbec . On decomposition in exponential Orlicz spaces. Math. Nachr., 213:7788, 2000.

  • [15]

    F. Farroni , A. Fiorenza and R. Giova . A sharp blow-up estimate for the Lebesgue norm. Rev. Mat. Complut., 32(3):745766, 2019.

  • [16]

    A. Fiorenza . Duality and reflexivity in grand Lebesgue spaces. Collect. Math., 51(2):131148, 2000.

  • [17]

    A. Fiorenza , M. R. Formica , A. Gogatishvili , T. Kopaliani and J.M. Rakotoson . Characterization of interpolation between grand, small or classical Lebesgue spaces. Nonlinear Anal., 177:422453, 2018.

    • Search Google Scholar
    • Export Citation
  • [18]

    A. Fiorenza , M. R. Formica , T. Roskovec and F. Soudsky . Gagliardo–Nirenberg inequality for rearrangement-invariant Banach function spaces. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 30(4):847864, 2019.

    • Search Google Scholar
    • Export Citation
  • [19]

    M. R. Formica , Y. V. Kozachenko , E. Ostrovsky and L. Sirota . Exponential Tail Estimates in the Law of Ordinary Logarithm (LOL) for Triangular Arrays of Random Variables. Lith. Math. J., 60(3):330358, 2020.

    • Search Google Scholar
    • Export Citation
  • [20]

    A. T. Gürkanli . Inclusions and the approximate identities of the generalized grand Le-besgue spaces. Turkish J. Math., 42(6):31953203, 2018.

    • Search Google Scholar
    • Export Citation
  • [21]

    B. Iaffei . Comparison of two weak versions of the Orlicz spaces. Rev. Un. Mat. Argentina, 40(1-2):191202, 1996.

  • [22]

    P. Jain , A. Molchanova , M. Singh and S. Vodopyanov . On grand Sobolev spaces and point-wise description of Banach function spaces. Nonlinear Anal., 202:112100, 17 pp., 2021.

    • Search Google Scholar
    • Export Citation
  • [23]

    P. Jain , M. Singh and A.P. Singh . Recent trends in grand Lebesgue spaces. In Function Spaces and Inequalities, volume 206 of Springer Proceedings in Mathematics & Statistics, pages 137159. Springer, 2017.

    • Search Google Scholar
    • Export Citation
  • [24]

    P. Jain , A. P. Singh , M. Singh and V.D. Stepanov . Sawyer’s duality principle for grand Lebesgue spaces. Math. Nachr., 292(4):841849, 2019.

    • Search Google Scholar
    • Export Citation
  • [25]

    Y. Jiao , L. Wu and L. Peng . Weak Orlicz-Hardy martingale spaces. Internat. J. Math., 26(8):1550062, 26 pp., 2015.

  • [26]

    R. Kawasumi and E. Nakai . Pointwise multipliers on weak Orlicz spaces. Hiroshima Math. J., 50(2):169184, 2020.

  • [27]

    Yu. V. Kozachenko and E. I. Ostrovsky . Banach Spaces of random variables of sub-Gaussian type. Teor. Veroyatn. Mat. Stat., Kiev„ 32(134):4253, 1985. (In Russian. English translation: Theory Probab. Math. Stat., 32:45–56, 1986.)

    • Search Google Scholar
    • Export Citation
  • [28]

    Yu. V. Kozachenko , E. I. Ostrovsky and L. Sirota . Relations between exponential tails, moments and moment generating functions for random variables and vectors. arXiv:1701.01901v1 [math.FA] 8 Jan 2017.

    • Search Google Scholar
    • Export Citation
  • [29]

    Yu. V . Kozachenko and M. Sergiienko. Estimates of distributions for some functionals of stochastic processes from an Orlicz space. Random Oper. Stoch. Equ., 22(2):6572, 2014.

    • Search Google Scholar
    • Export Citation
  • [30]

    M. A. Krasnosel’ski˘i and Ja. B. Ruticki˘i . Convex Functions and Orlicz Spaces. P. Noordhoff Ltd, Groningen, 1961.

  • [31]

    K. Leśnik and J. Tomaszewski . Pointwise multipliers of Orlicz function spaces and factor-ization. Positivity, 21(4):15631573, 2017.

    • Search Google Scholar
    • Export Citation
  • [32]

    E. H. Lieb and M. Loss . Analysis. Second edition. American Mathematical Society, Providence, RI 2001.

  • [33]

    N. Liu and Y. Ye . Weak Orlicz space and its convergence theorems. Acta Math. Sci. Ser. B, 30(5):14921500, 2010.

  • [34]

    P. Liu , Y. Hou and M. Wang . Weak Orlicz space and its applications to the martingale theory. Sci. China Math., 53(4):905916, 2010.

    • Search Google Scholar
    • Export Citation
  • [35]

    P. Liu and M. Wang . Weak Orlicz spaces: some basic properties and their applications to harmonic analysis. Sci. China Math., 56(4):789802, 2013.

    • Search Google Scholar
    • Export Citation
  • [36]

    G. G. Lorentz . Some new functional spaces. Ann. of Math., 51(2):3755, 1950.

  • [37]

    G. G. Lorentz . On the theory of spaces Λ. Pacific J. Math., 1(3):411429, 1951.

  • [38]

    G. G. Lorentz . Relations between function spaces. Proc. Amer. Math. Soc., 12(1):127132, 1961.

  • [39]

    L. Maligranda . Orlicz spaces and interpolation. Seminários de Matemática, Universidade Estadual de Campinas, Departamento de Matemática, Campinas, 1989.

    • Search Google Scholar
    • Export Citation
  • [40]

    L. Maligranda and E. Nakai . Pointwise multipliers of Orlicz spaces. Arch. Math. (Basel), 95(3):251256, 2010.

  • [41]

    A. A. Masta , H. Gunawan and W.Setya. Budhi . Inclusion Properties of Orlicz and Weak Orlicz Spaces. J. Math. Fundam. Sci., 48(3):193203, 2016.

    • Search Google Scholar
    • Export Citation
  • [42]

    A. Molchanova . A note on the continuity of minors in grand Lebesgue spaces. J. Fixed Point Theory Appl., 21(2):Paper no. 49, 13 pp., 2019.

    • Search Google Scholar
    • Export Citation
  • [43]

    E. I. Ostrovsky . Exponential Estimations for Random Fields, (Russian), Moscow-Obninsk, OINPE, 1999.

  • [44]

    E. I. Ostrovsky . Bide-side exponential and moment inequalities for tail of distributions of polynomial martingales. arXiv:math/0406532v1 [math.PR] 25 Jun 2004.

    • Search Google Scholar
    • Export Citation
  • [45]

    E.I. Ostrovsky and L. Sirota . Moment Banach spaces: theory and applications. HIAT Journal of Science and Engineering, C, Vol., 4(1-2):233262, 2007.

    • Search Google Scholar
    • Export Citation
  • [46]

    E. I. Ostrovsky and L. Sirota . Individual lower bounds for Calderon’s generalized Lorentz norm estimates. arXiv:1210.4832v1 [math.FA] 17 Oct 2012.

    • Search Google Scholar
    • Export Citation
  • [47]

    L. Pick , A. Kufner , O. John and S. Fučík . Function Spaces, Volume 1, 2nd Revised and Extended Edition. De Gruyter Series in Nonlinear Analysis and Applications 14, De Gruyter, Berlin 2013.

    • Search Google Scholar
    • Export Citation
  • [48]

    M. M. Rao and Z.D. Ren . Theory of Orlicz Spaces. New York: Marcel Dekker Inc, 1991.

  • [49]

    M. M. Rao and Z.D. Ren . Applications of Orlicz Spaces. New York: Marcel Dekker Inc, 2002.

  • [50]

    J. Soria . Lorentz spaces of weak type. Quart. J. Math. Oxford (2), 49(193):93103, 1998.

  • [51]

    E. Stein and G. Weiss . Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971.

  • [52]

    A. Torchinsky . Interpolation of operators and Orlicz classes. Studia Math., 59(2):177207. 1976/77.

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