Approximation by Nörlund and Riesz means in weighted Lebesgue space with variable exponent

Year 2019, Volume: 68 Issue: 2, 2014 - 2025, 01.08.2019

Ahmet Testici

https://doi.org/10.31801/cfsuasmas.460449

Cited By: 1

Abstract

We investigate the approximation properties of Nörlund and Riesz means of trigonometric Fourier series are investigated in the subset of weighted Lebesgue space with variable exponent.

Keywords

Weighted Lebesgue space with variable exponent, Lipschitz class, Riesz mean, Muckenhoupt weight, Nörlund means

Supporting Institution

TUBITAK

Project Number

114F422

References

• Akgun R., Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth, Georgian Math. Journal 18, (2011), 203-235.
• Akgun R. and Kokilashvili V., The refined direct and converse inequalities of trigonometric approximation in weighted variable exponent Lebesgue space, Georgian Mathematical Journal 18, No: 3, (2011), 399-423.
• Cruz-Uribe, D. V. and Fiorenza, A., Variable Lebesgue Spaces Foundation and Harmonic Analysis. Birkhäsuser, 2013
• Diening L, Harjulehto P., Hästö, P., Růžička, M., Lebesgue and Sobolev Spaces with Variable Exponents, Springer, Heidelberg Dordrecht London New York; 2011.
• Sharapudinov, I. I, Some questions of approximation theory in the Lebesgue spaces with variable exponent , Viladikavkaz, 2012.
• Timan A. F., Theory of Approximation of Functions of a Real Variable:New York : Macmillan, 1963.
• Cruz-Uribe D. V., Diening L., Hästö P., The maximal operator on weighted variable Lebesgue spaces, Fractional Calculus and Applied Analysis 14, No 3, (2011), 361-374.
• Quade E. S., Trigonometric approximation in the mean. Duke Math. J. 3 (1937), No. 3, 529--543.
• R.N. Mohapatra R. N., Russell D. C., Some direct and inverse theorems in approximation of functions, J. Austral. Math. Soc. (Ser. A) 34 (1983), 143-154.
• Chandra P., A note on degree of approximation by Nörlund and Riesz operators, Mat. Vesn. 42, (1990), 9-10.
• Chandra P., Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275, Issue 1, (2002), 13-26.
• Leindler L., Trigonometric approximation in L_{p} -norm, Journal of Mathematical Analysis and Applications 302 (1), (2005), 129-136.
• Guven A., Trigonometric Approximation Of Functions In Weighted L^{p }Spaces, Sarajevo Journal Of Mathematics 5 (17), (2009), 99-108.
• Guven A., Approximation In Weighted L^{p} Space, Revista De La Unión Mathemática Argentina 53, No 1, (2012), 11-23.
• Guven A. and Israfilov D. M., Trigonometric Approximation in Generalized Lebesgue Spaces L^{p(x)}, Journal of Math. Inequalities 4, No 2, (2010), 285-299.
• Guven A., Trigonometric Approximation By Matrix Transforms in L^{p(x)} Space, Analysis and Applications 10, No 1, (2012), 47-65.
• Israfilov D., Kokilashvili V., Samko S., Approximation In Weighted Lebesgue and Smirnov Spaces With Variable Exponents, Proceed. of A. Razmadze Math. Institute 143, (2007), 25-35.
• Israfilov, D. M. and Testici, A., Trigonometric Approximation by Matrix Transforms in Weighted Lebesgue Spaces with Variable Exponent, Results in Mathematics 73 : 8, Issue 1, (2018).
• D. M. Israfilov and Ahmet Testici, Some Inverse Theorem of Approximation Theory in Weighted Lebesgue Space With Variable Exponent, Analysis Mathematica 44(4), (2018), 475-492.
• Deger U., On Approximation By Nörlund and Riesz Submethods In Variable Exponent Lebesgue Spaces, Commun.Fac.Sci.Univ.Ank.Series A1 67, No 1, (2018), 46-59.
• Yildirir Y. E. and Avsar A. H, Approximation of periodic functions in weighted Lorentz spaces, Sarajevo Journal Of Mathematics 13 (25), (2017), 49-60.