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Year 2020, Volume: 6 Issue: 1, 32 - 36, 29.06.2020
https://doi.org/10.23884/mejs.2020.6.1.04

Abstract

References

  • [1] Hudzik, H., “The problems of separability, duality, reflexivity and of comparison for generalized Orlicz–Sobolev spaces ”, Commentationes Mathematicae, 21, 315–324, 1979.
  • [2] Musielak, J., Orlicz spaces and modular spaces, Springer, Berlin Heidelberg New York, 1983.
  • [3] Orlicz, W., “Über konjugierte Exponentenfolgen”, Studia Mathematica, 3, 200–212, 1931.
  • [4] Růžička, M., Elektrorheological fluids: modeling and mathematical theory, Springer-Verlag, Berlin, 2000.
  • [5] Acerbi, E., Mingione, G., “Regularity results for stationary electro-rheological fluids”, Archive for Rational Mechanics and Analysis, 164(3), 213-259, 2002.
  • [6] Aboulaich, R., et al., “New diffusion models in image processing”, Computers & Mathematics with Applications, 56, 4, 874-882, 2008.
  • [7] Chen, Y., et al., “Variable exponent, linear growth functionals in image restoration” SIAM journal on Applied Mathematics, 66, 4, 1383-1406, 2006.
  • [8] Zhikov , V.V., “Meyer-type estimates for solving the nonlinear Stokes system”, Differential Equations, 33, 1, 108–115, 1997.
  • [9] Amaziane, B., et al., “Nonlinear flow through double porosity media in variable exponent Sobolev spaces”, Nonlinear Analysis: Real World Applications, 10, 4, 2521-2530, 2009.
  • [10] Kováčik, O., Rákosník, J., “On spaces and ”, Czechoslovak Mathematical Journal, 41, 4, 592-618, 1991.
  • [11] Diening, L., et al., M., Lebesgue and Sobolev spaces with variable exponents, Springer, 2011.
  • [12] Cruz-Uribe, D.V., Fiorenza, A., Variable Lebesgue spaces: foundations and harmonic analysis, Springer Science & Business Media, 2013.
  • [13] Harjulehto, P., Hasto, P., “Lebesgue points in variable exponent spaces”, Annales Academiæ Scientiarium Fennicæ. Mathematica, 29, 295–306, 2004.

A REVERSE HÖLDER INEQUALITY IN L^p(x)(Ω)

Year 2020, Volume: 6 Issue: 1, 32 - 36, 29.06.2020
https://doi.org/10.23884/mejs.2020.6.1.04

Abstract



In this study, at first we provide
a general overview 
of L^p(x)(Ω) spaces, also known as variable exponent
Lebesgue spaces. They are a generalization of classical Lebesgue spaces L^p
 in the sense that
constant exponent replaced by a measurable function
.  Then, based on classical Lebesgue space
approach
we prove a reverse of Hölder inequality in L^p(x)(Ω)
. Therefore, our proof in variable
exponent Lebesgue space is very
similar to that in classical Lebesgue space.




References

  • [1] Hudzik, H., “The problems of separability, duality, reflexivity and of comparison for generalized Orlicz–Sobolev spaces ”, Commentationes Mathematicae, 21, 315–324, 1979.
  • [2] Musielak, J., Orlicz spaces and modular spaces, Springer, Berlin Heidelberg New York, 1983.
  • [3] Orlicz, W., “Über konjugierte Exponentenfolgen”, Studia Mathematica, 3, 200–212, 1931.
  • [4] Růžička, M., Elektrorheological fluids: modeling and mathematical theory, Springer-Verlag, Berlin, 2000.
  • [5] Acerbi, E., Mingione, G., “Regularity results for stationary electro-rheological fluids”, Archive for Rational Mechanics and Analysis, 164(3), 213-259, 2002.
  • [6] Aboulaich, R., et al., “New diffusion models in image processing”, Computers & Mathematics with Applications, 56, 4, 874-882, 2008.
  • [7] Chen, Y., et al., “Variable exponent, linear growth functionals in image restoration” SIAM journal on Applied Mathematics, 66, 4, 1383-1406, 2006.
  • [8] Zhikov , V.V., “Meyer-type estimates for solving the nonlinear Stokes system”, Differential Equations, 33, 1, 108–115, 1997.
  • [9] Amaziane, B., et al., “Nonlinear flow through double porosity media in variable exponent Sobolev spaces”, Nonlinear Analysis: Real World Applications, 10, 4, 2521-2530, 2009.
  • [10] Kováčik, O., Rákosník, J., “On spaces and ”, Czechoslovak Mathematical Journal, 41, 4, 592-618, 1991.
  • [11] Diening, L., et al., M., Lebesgue and Sobolev spaces with variable exponents, Springer, 2011.
  • [12] Cruz-Uribe, D.V., Fiorenza, A., Variable Lebesgue spaces: foundations and harmonic analysis, Springer Science & Business Media, 2013.
  • [13] Harjulehto, P., Hasto, P., “Lebesgue points in variable exponent spaces”, Annales Academiæ Scientiarium Fennicæ. Mathematica, 29, 295–306, 2004.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Article
Authors

Yasin Kaya 0000-0002-7779-6903

Publication Date June 29, 2020
Submission Date November 18, 2019
Acceptance Date June 18, 2020
Published in Issue Year 2020 Volume: 6 Issue: 1

Cite

IEEE Y. Kaya, “A REVERSE HÖLDER INEQUALITY IN L^p(x)(Ω)”, MEJS, vol. 6, no. 1, pp. 32–36, 2020, doi: 10.23884/mejs.2020.6.1.04.

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