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Generalized Laplace Transform Inequalities in Multiple Weighted Orlicz Spaces

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Computation, Cryptography, and Network Security
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Abstract

In this paper we use quite different new methods to establish some new generalized Laplace transform inequalities in the multiple weighted Orlicz spaces. They are significant improvements and generalizations of many famous results.

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References

  1. Widder, D.V.: The Laplace Transform. Princeton University Press, Princeton (1972)

    Google Scholar 

  2. Wolff, K.B.: Integral Transforms in Science and Engineering. Plenum, New York (1979)

    Book  Google Scholar 

  3. Zauderer, E.: Partial Differential Equations of Applied Mathematics. A Wiley-Interscience. Wiley, New York (1983)

    MATH  Google Scholar 

  4. Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Dover, New York (1986)

    Google Scholar 

  5. Hardy, G.H.: The constants of certain inequalities. J. Lond. Math. Soc. 8, 114–119 (1933)

    Article  Google Scholar 

  6. Kovacik, O., Rakosnik, J.: On spaces L p(x) and W 1, p(x). Czechoslo. Math. J. 41(116), 592–618 (1991)

    MathSciNet  Google Scholar 

  7. Fhan, X.L., Zhao, D.: On the spaces L p(x) and W k, p(x). J. Math. Anal. Appl. 263, 424–446 (2001)

    Article  MathSciNet  Google Scholar 

  8. Edmunds, D.E., Kokilashvili, V., Meskhi, A.: On the boundedness and compactness of the weighted Hardy operators in L p(x) spaces. Georgian Math. J. 12(1), 126–130 (2005)

    MathSciNet  Google Scholar 

  9. Diening, L., Samko, S.: Hardy inequality in variable eponent Lebesgue spaces. Fract. Calc. Appl. Anal. 10(1), 1–17 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Kopaliam, T.: Interpolation theorems for variable exponent Lebesgue space. J. Funct. Anal. 257, 3541–3551 (2009)

    Article  MathSciNet  Google Scholar 

  11. Mamedov, F.I., Harman, A.: On a weighted inequality of Hardy type in spaces L p(⋅ ). J. Math. Anal. Appl. 353, 521–530 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jichang, K., Debnath, L.: On Hilbert’s type inequalities on the weighted Orlicz spaces. Pac. J. Appl. Math. 1(1), 89–97 (2008)

    MathSciNet  Google Scholar 

  13. Maligranda, L.: Orlicz spaces and interpolation. IMECC (1989)

    Google Scholar 

  14. Strömberg, J.O.: Bounded mean oscillations with Orlicz norms and duality of Hardy spaces. Indiana Univ. Math. J. 28(3), 511–544 (1979)

    Article  MathSciNet  Google Scholar 

  15. Zwillinger, D.: Handbook of Integration. Springer, New York (1992)

    MATH  Google Scholar 

  16. Kuang, J.C.: Generalized Hardy-Hilbert type inequalities on multiple weighted Orlicz spaces. In: Handbook of Functional Equations: Functional Inequalities. Springer Optimizations and Its Applications, vol. 95, pp. 273–280. Springer, Berlin (2014)

    Google Scholar 

  17. Jichang, K.: Applied Inequalities, 4th edn. Shandong Science and Technology Press, Jinan (2010) (in Chinese)

    Google Scholar 

  18. Kuang, J.C.: Real and Functional Analysis (Continuation), vol. 2. Higher Education Press, Beijing (2015) (in Chinese)

    Google Scholar 

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Acknowledgements

Foundation item: This work is supported by the Natural Science Foundation of China (No. 11271123).

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Correspondence to Jichang Kuang .

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Kuang, J. (2015). Generalized Laplace Transform Inequalities in Multiple Weighted Orlicz Spaces. In: Daras, N., Rassias, M. (eds) Computation, Cryptography, and Network Security. Springer, Cham. https://doi.org/10.1007/978-3-319-18275-9_13

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