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Exact Calculation of Sums of Cones in Lorentz Spaces

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Abstract

A method for exactly calculating norm on the sum of the cones of nonincreasing or concave functions in Lorentz spaces is proposed. The obtained result makes it possible to prove new extrapolation theorems for cones in Lorentz, Lebesgue, and Marcinkiewicz spaces with exact constants.

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References

  1. A. Fiorenza, Collect. Math., 51:2 (2000), 131–148.

    MathSciNet  Google Scholar 

  2. A. Fiorenza and G. E. Karadzhov, Z. Anal. Anwend., 23:4 (2004), 657–681.

    Article  Google Scholar 

  3. M. Ari˜no and B. Muckenhoupt, Trans. Amer. Math. Soc., 320:2 (1990), 727–735.

    MathSciNet  Google Scholar 

  4. E. Sawyer, Studia Math., 96:2 (1990), 145–158.

    Article  MathSciNet  Google Scholar 

  5. E. I. Berezhnoi, Trudy Mat. Inst. Steklov., 204 (1993), 3–34. English transl.: Proc. Steklov Inst. Math., 3(204) (1994), 1–25.

    Google Scholar 

  6. E. I. Berezhnoi and L. Maligranda, Dokl. Ross. Akad. Nauk, 406:4 (2006), 43–442. English transl.: Russian Acad. Sci. Dokl. Math., 73:1 (2006), 59–62.

    Google Scholar 

  7. A. Gogatishvili and V. D. Stepanov, Uspekhi Mat. Nauk, 68:4 (2013), 3–68. English transl.: Russian Math. Surveys, 68:4 (2013), 597–664.

    Article  MathSciNet  Google Scholar 

  8. S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators, Translation of Mathematical Monographs, vol. 54, Amer. Math. Soc., Providence, RI, 1982.

  9. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I, II, Springer-Verlag, Berlin–New York, 1979.

    Book  MATH  Google Scholar 

  10. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988.

    MATH  Google Scholar 

  11. M. Milman, Extrapolation and Optimal Decompositions with Applications to Analysis, Lecture Notes in Math., vol. 1580, Springer-Verlag, Berlin, 1994.

  12. G. E. Karadzhov and M. Milman, J. Approx. Theory, 133:1 (2005), 38–99.

    Article  MathSciNet  Google Scholar 

  13. M. J. Carro, A. N. Marcoci, and L. G. Marcoci, J. Approx. Theory, 164:5 (2012), 776–790.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Yaroslavl State University, Yaroslavl, Russia

    E. I. Berezhnoi

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  1. E. I. Berezhnoi
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Correspondence to E. I. Berezhnoi.

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 2, pp. 66–71, 2018

Original Russian Text Copyright © by E. I. Berezhnoi

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Berezhnoi, E.I. Exact Calculation of Sums of Cones in Lorentz Spaces. Funct Anal Its Appl 52, 134–138 (2018). https://doi.org/10.1007/s10688-018-0218-3

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  • DOI: https://doi.org/10.1007/s10688-018-0218-3

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