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Journals / Turkish Journal of Mathematics and Computer Science / 2019 / Cilt: 11 - Sayı: -

Vector-Valued Weighted Sobolev Spaces with Variable Exponent

Ismail Aydın
Pages
123–131
Publication Date
2022-11-04
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally under some conditions we will investigate some basic properties ofvector-valued weighted variable exponent Sobolev spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Our aim is to introduce the vector-valued weighted variable exponent Lebesgue spaces.
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Key Findings & Data:We discusstwo different type of Holder inequalities in this spaces.
💡
Conclusion & Impact:Finally under some conditions we will investigate some basic properties ofvector-valued weighted variable exponent Sobolev spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Our aim is to introduce the vector-valued weighted variable exponent Lebesgue spaces. We discusstwo different type of Holder inequalities in this spaces. We will also show that every elements of vector-valued ¨weighted variable exponent Lebesgue spaces are locally integrable. Hence we can define vector-valued weightedvariable exponent Sobolev spaces. Finally under some conditions we will investigate some basic properties ofvector-valued weighted variable exponent Sobolev spaces.

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Cite This Article

Aydın, I. (2022). Vector-Valued Weighted Sobolev Spaces with Variable Exponent. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: -, 123–131. https://ajindex.com/articles/609146

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References (14)

  1. Amann, H., Linear and Quasilinear Parabolic Problems, Vol. I: Abstract Linear Theory, Birkhauser, Basel, 1995
  2. Amann, H., Operator-valued Fourier multipliers, vector-valued Besov spaces and applications, Math. Nachr., 186(1997), 5–56
  3. Aydın, I., Weighted variable Sobolev spaces and capacity, J Funct Space Appl, 2012(2012), Article ID 132690, 17 pages, doi:10.1155/2012/132690
  4. Cartan, H., Differential calculus, Hermann, Paris-France, 1971
  5. Cheng, C., Xu, J., Geometric properties of Banach space valued Bochner-Lebesgue spaces with variable exponent, J Math Inequal, 7(3)(2013), 461–475
  6. Cruz-Uribe, D., Fiorenza, A., Variable Lebesgue Spaces: Foundations and Harmonic Analysis (Applied and Numerical Harmonic Analysis), Birkhauser /Springer, Heidelberg, 2013
  7. Diening, L., Maximal function on generalized Lebesgue spaces Lp(.), Math. Inequal. Appl., 7(2)(2004), 245–253
  8. Diening, L., Harjulehto, P., Hast o, P., Ruzicka, M., Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, vol. 2017, Springer, Heidelberg, 2011
  9. Diestel, J., UHL, J.J., Vector measures, Amer Math Soc, 1977
  10. Edmunds, E., Fiorenza, A., Meskhi, A., On a measure of non-compactness for some classical operators, Acta Math. Sin., 22(6)(2006), 1847–1862
  11. Konig, H., Eigenvalue Distribution of Compact Operators, Birkhauser, Basel, 1986
  12. Kovacik, O., Rakosnik, J., On spaces Lp(x) and Wk,p(x), Czech. Math. J., 41(116)(1991), 592–618
  13. Pietsch, A., Eigenvalues and S-numbers, Cambridge Univ. Press, Cambridge, 1987
  14. Pruss, J., Evolutionary Integral Equations and Applications, Birkhauser, Basel, 1993.