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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 11 Special Issue

Vector-Valued Weighted Sobolev Spaces with Variable Exponent

İsmail Aydın0000-0001-8371-3185
Pages
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Publication Date
2019-12-30
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 of vector-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 discuss two different type of H\"{o}lder inequalities in this spaces.
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Conclusion & Impact:Finally under some conditions we will investigate some basic properties of vector-valued weighted variable exponent Sobolev spaces.
🔬Design:Conference Paper
📍Scope:Comprehensive Sample
⚙️Variables:Vector-valued weighted variable Sobolev spaces · Hölder inequality · Radon-Nikodym property

Abstract

Our aim is to introduce the vector-valued weighted variable exponent Lebesgue spaces. We discuss two different type of H\"{o}lder 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 weighted variable exponent Sobolev spaces. Finally under some conditions we will investigate some basic properties of vector-valued weighted variable exponent Sobolev spaces.

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Cite This Article

Aydın, İ. (2019). Vector-Valued Weighted Sobolev Spaces with Variable Exponent. Turkish Journal of Mathematics and Computer Science, Volume: 11 Special Issue. https://ajindex.com/articles/1324881

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References (14)

  1. Amann, H., Linear and Quasilinear Parabolic Problems, Vol. I: Abstract Linear Theory, Birkh\"{a}user, Basel, 1995.
  2. Amann, H., {\em Operator-valued Fourier multipliers, vector-valued Besov spaces and applications}, Math. Nachr., \textbf{186}(1997), 5--56.
  3. Ayd\i n, I., {\em Weighted variable Sobolev spaces and capacity}, J Funct Space Appl, \textbf{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., {\em Geometric properties of Banach space valued Bochner-Lebesgue spaces with variable exponent}, J Math Inequal, \textbf{7(3)}(2013), 461--475.
  6. Cruz-Uribe, D., Fiorenza, A., Variable Lebesgue Spaces: Foundations and Harmonic Analysis (Applied and Numerical Harmonic Analysis), Birkh\"{a}user/Springer, Heidelberg, 2013.
  7. Diening, L., {\em Maximal function on generalized Lebesgue spaces $L^{p(.)}$}, Math. Inequal. Appl., \textbf{7(2)}(2004), 245--253.
  8. Diening, L., Harjulehto, P., H\"{a}st\"{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., {\em On a measure of non-compactness for some classical operators}, Acta Math. Sin., \textbf{22(6)}(2006), 1847--1862.
  11. K\"{o}nig, H., Eigenvalue Distribution of Compact Operators, Birkh\"{a}user, Basel, 1986.
  12. Kov\'{a}\v{c}ik, O., R\'{a}kosnik, J., {\em On spaces $L^{p(x)}$ and $W^{k,p(x)}$}, Czech. Math. J., \textbf{41(116)}(1991), 592--618.
  13. Pietsch, A., Eigenvalues and S-numbers, Cambridge Univ. Press, Cambridge, 1987.
  14. Pr\"{u}ss, J., Evolutionary Integral Equations and Applications, Birkh\"{a}user, Basel, 1993.