Approximation of Periodic Functions in Weighted Lorentz Spaces

Authors

  • Yunus Emre Yildirir
  • Ahmet Hamdi Avsar

DOI:

https://doi.org/10.5644/SJM.13.1.03

Keywords:

Weighted Lorentz space, Muckenhoupt weight, modulus of continuity, Fourier series

Abstract

In the present work, the approximation properties of means of trigonometric Fourier series in weighted Lorentz spaces with weights satisfying the so called Muckenhoupt's $A_{p}$ conditions are investigated.

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References

C. Bennet and R. Sharpley, Interpolation of Operators, Academic Press, Inc., Boston, MA, 1968.

P. Chandra, Approximation by Nörlund operators, Mat. Vesn., 38 (1986), 263--269.

P. Chandra, Functions of classes $L_{p}$ and $Lip(alpha ,p)$ and their Riesz means, Riv. Mt. Univ. Parma, (4) 12 (1986), 275--282.

P. Chandra, A note on degree of approximation by Nörlund and Riesz operators, Mat. Vesn., 42 (1990), 9--10.

P. Chandra, Trigonometric approximation of functions in $L_{p}$ norm}, J. Math. Anal. Appl., 275 (2002), 13--26.

H. M. Chang, R. A. Hunt and D. S. Kurtz, The Hardy-Littlewood maximal functions on $L(p,q)$ spaces with weights, Indiana Univ. Math. J. 31 (1982), 109--120.

V. T. Gavriljuk and S. B. Stečkin, Approximation of continuous functions by Fourier sums, (Russian) Akad. Nauk Ukrain. SSR Inst. Mat., Preprint No. 1 (1979), 44 pp.

A. Guven, Trigonomeric approximations of functions in weighted $L_{p}$ spaces}, Sarajevo J. Math., 5 (1) (2009), 99--108.

A. Guven and D. M. Israfilov, On approximation in weighted Orlicz spaces, Math. Slovaca, 62 (1) (2012), 77--86.

I. Genebashvili, A. Gogatishvili, V. Kokilashvili and M. Krbec, Weight theory for Integral Transforms on Spaces of Homogeneous Type, Longman, 1998.

V. Kokilashvili and M. Krbec, Weighted Inequalities in Lorentz and Orlicz Spaces, World Scientific Publishing Co. Inc. River Edge, NJ, 1991.

V. Kokilashvili and Y. E. Yildirir, On the approximation by trigonometric polynomials in weighted Lorentz spaces, J. Funct. Spaces Appl., 8 (2010), 67--86.

N. X. Ky, Moduli of mean smoothness and approximation with Ap-weights, Ann. Univ. Sci. Budap., 40 (1997), 37--48.

L. Leindler, Trigonometric approximation in }$L_{p}$, J. Math. Anal. Appl., 302 (2005), 129--136.

R. N. Mohapatra and D. C. Russell, Some direct and inverse theorems in approximation of functions, J. Aust. Math. Soc. (Ser. A) 34 (1983), 143--154.

B. Muckenhoupt, Weighted Norm Inequalities for the Hardy Maximal Function, Trans. Amer. Math. Soc., 165 (1972), 207--226.

Quade, E. S., Trigonometric approximation in the mean, Duke Math. J., (1937), 529-542.

M. F. Tīman, The absolute Cesàro summability of orthogonal Fourier series, (Russian) Ural. Gos. Univ. Mat. Zap., 6 (4) (1968), 109--113.

P. L. Ulyanov, On approximation of functions, Sib. Mat. Zh., 5 (2) (1964).

Y. E. Yildirir and D. M. Israfilov, Approximation theorems in weighted Lorentz spaces, Carpathian J. Math. 26 (2010), 108--119.

A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Cambridge, 1968.

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Published

19.05.2017

How to Cite

Yildirir, Y. E. ., & Avsar, A. H. . (2017). Approximation of Periodic Functions in Weighted Lorentz Spaces. Sarajevo Journal of Mathematics, 13(1), 49–60. https://doi.org/10.5644/SJM.13.1.03

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