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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 1

Weighted variable exponent grand Lebesgue spaces and inequalities of approximation

İsmail Aydın
Ramazan Akgün
Pages
199–215
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

We also prove the direct and inverse theorems in these spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we discuss and investigate trigonometric approximation in weighted grand variable exponent Lebesgue spaces.
📊
Key Findings & Data:In this paper we discuss and investigate trigonometric approximation in weighted grand variable exponent Lebesgue spaces.
💡
Conclusion & Impact:We also prove the direct and inverse theorems in these spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:weighted grand variable exponent Lebesgue · Sobolev and Lipschitz space · maximal operator

Abstract

In this paper we discuss and investigate trigonometric approximation in weighted grand variable exponent Lebesgue spaces. We also prove the direct and inverse theorems in these spaces.

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Cite This Article

Aydın, İ., Akgün, R. (2022). Weighted variable exponent grand Lebesgue spaces and inequalities of approximation. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 1, 199–215. https://ajindex.com/articles/530001

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References (17)

  1. G. Anatriello, Iterated grand and small Lebesgue spaces, Collect. Math. 65, 273–284, 2014
  2. R. Akgün, Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent, Ukrainian Math. J. 63 (1), 1–26, 2011
  3. R. Akgün, Approximating polynomials for functions of weighted Smirnov-Orlicz spaces, J. Funct. Spaces Appl. 2012, Art. ID 982360, 2012
  4. R. Akgün and D.M. Israfilov, Approximation and moduli of smoothness of fractional order in Smirnov-Orlicz spaces, Glas. Mat. Ser. III, 42 (2), 121–136, 2008
  5. R. Akgün and D.M. Israfilov, Polynomial approximation in weighted Smirnov Orlicz space, Proc. A. Razmadze Math. Inst. 139, 89–92, 2005
  6. R. Akgün and D.M. Israfilov, Approximation by interpolating polynomials in Smirnov- Orlicz class, J. Korean Math. Soc. 43 (2), 413–424, 2006
  7. R. Akgün and D.M. Israfilov, Simultaneous and converse approximation theorems in weighted Orlicz spaces, Bull. Belg. Math. Soc. 17 (2), 13–28, 2010
  8. R. Akgün and V. Kokilashvili, On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces, Banach J. Math. Anal. 5 (1), 70-82, 2011
  9. I. Aydin, Weighted variable Sobolev spaces and capacity, J. Funct. Spaces Appl. 2012, Art. ID 132690, 2012
  10. D. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces: Foundations and Har- monic Analysis (Applied and Numerical Harmonic Analysis), Birkhäuser/Springer, Heidelberg, 2013
  11. D. Cruz-Uribe, L. Diening and P. Hästö, The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14 (3), 361–374, 2011
  12. N. Danelia and V. Kokilashvili, Approximation by trigonometric polynomials in the framework of variable exponent Lebesgue spaces, Georgian Math. J. 23 (1), 43–53, 2016
  13. L. Diening, Maximal function on generalized Lebesgue spaces Lp(.), Math. Inequal. Appl. 7, 245–253, 2004
  14. L. Diening, P. Harjulehto, P. Hästö and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, 2017, Springer, Heidelberg, 2011
  15. V.K. Dzyadyk and I.A. Shevchuk, Theory of Uniform Approximation of Functions by Polynomials, Walter de Gruyter GmbH & Co. KG, 10785 Berlin, Germany, 2008
  16. A. Fiorenza, B. Gupta and P. Jain, The maximal theorem in weighted grand Lebesgue spaces, Studia Math. 188 (2), 123–133, 2008
  17. A. Fiorenza, V. Kokilashvili and A. Meskhi, Hardy-Littlewood maximal operator in weighted grand variable exponent Lebesgue space, Mediterr.