SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

Linear methods of approximation in weighted Lebesgue spaces with variable exponent

Ahmet TESTİCİ
Daniyal M. ISRAFILOV
Pages
744–753
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Main results are new even in the nonweighted variable exponent Lebesgue spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Some estimations in below for the deviations conducted by the Zygmund means and by the Abel-Poisson sums in the weighted Lebesgue spaces with variable exponent are obtained.
📊
Key Findings & Data:In the classical Lebesgue spaces these estimations were proved by M.
💡
Conclusion & Impact:Main results are new even in the nonweighted variable exponent Lebesgue spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Zygmund means · Fejér means · Abel-Poisson means

Abstract

Some estimations in below for the deviations conducted by the Zygmund means and by the Abel-Poisson sums in the weighted Lebesgue spaces with variable exponent are obtained. In the classical Lebesgue spaces these estimations were proved by M. F. Timan. The considered weight functions satisfy the well known Muckenhout condition. For the proofs of main results some estimations obtained in the classical weighted Lebesgue spaces and also an extrapolation theorem proved in the weighted variable exponent Lebesgue spaces are used. Main results are new even in the nonweighted variable exponent Lebesgue spaces.

🔖

Cite This Article

TESTİCİ, A., ISRAFILOV, D. M. (2022). Linear methods of approximation in weighted Lebesgue spaces with variable exponent. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 744–753. https://ajindex.com/articles/529539

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. R. Akgun, Trigonometric Approximation of Functions in Generalized Lebesgue Spaces With Variable Exponent, Ukrainian Math. J. 63 (1), 3–23, 2011
  2. R. Akgun, Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth, Georgian Math. J. 18, 203–235, 2011
  3. B.T. Bilalov and Z.G. Guseynov, Basicity of a system of exponents with a piece-wise linear phase in variable spaces, Mediterr. J. Math. 9 (3), 487–498, 2012
  4. D.V. Cruz-Uribe, L. Diening and P. Hästö, The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14 (3), 361–374, 2011
  5. D.V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces Foundation and Har- monic Analysis, Birkhäsuser, 2013
  6. D.V. Cruz Uribe and D.L. Wang, Extrapolation and weighted norm inequalities in the variable Lebesgue spaces, Trans. Amer. Math. Soc. 369 (2), 1205–1235, 2017
  7. L. Diening and M. Růžiˆcka, Calderon-Zygmund operators on generalized Lebesgue spaces $L^{p\left( x\right) }$ and problems related to fluid dynamic, J. Reine Angew. Math. 563, 197– 220, 2003
  8. A. Guven, Trigonometric Approximation By Matrix Transforms in $L^{p\left( x\right) }$ Space, Anal. Appl. 10 (1), 47–65, 2012
  9. A. Guven and D.M. Israfilov, Trigonometric Approximation in Generalized Lebesgue Spaces $L^{p\left( x\right) }$, J. Math. Inequal. 4 (2), 285–299, 2010
  10. D.M. Israfilov and A. Testici, Approximation in Smirnov Classes with Variable Exponent, Complex Var. Elliptic Equ. 60(9), 1243–1253, 2015
  11. D.M. Israfilov and A. Testici, Approximation by Matrix Transforms in Weighted Lebesgue Spaces with Variable Exponent, Results Math. 73 (8), 2018,
  12. D.M. Israfilov, V. Kokilashvili and S.G. Samko, Approximation In Weighted Lebesgue and Smirnov Spaces With Variable Exponents, Proceed. of A. Razmadze Math. Insti- tute, 143, 25–35, 2007
  13. S.Z. Jafarov, Linear Methods for Summing Fourier Series and Approximation in Weighted Lebesgue Spaces with Variable Exponents, Ukrainian Math. J. 66 (10), 1509– 1518, 2015
  14. S.Z. Jafarov, Approximation by trigonometric polynomials in subspace of variable ex- ponent grand Lebesgue spaces, Global Journal of Mathematics, 8 (2), 836–843, 2016
  15. S.Z. Jafarov, Linear methods of summing Fourier series and approximation in weighted Orlicz spaces, Turkish J. Math. 42 (6), 2916–2925, 2018
  16. A. Kamińska, Indices, convexity and concavity in Musileak-Orlicz spaces, Funct. Ap- p