Trigonometric Approximation of Functions in Weighted $\boldsymbol{L^{p}}$ Spaces

Authors

  • Ali Guven Department of Mathematics, Faculty of Art and Science, Balikesir University, Balikesir, Turkey

DOI:

https://doi.org/10.5644/SJM.05.1.09

Keywords:

Lipschitz class, means of Fourier series, Muckenhoupt class, weighted $L^{p}$ space

Abstract

The approximation properties of means of trigonometric Fourier series in weighted $L^{p}$ spaces $ \left( 1<p<\infty \right) $ with Muckenhoupt weights are investigated.

 

2000 Mathematics Subject Classification. 41A25, 42A10

Downloads

Download data is not yet available.

References

P. Chandra, Approximation by N¨orlund operators, Mat. Vesn., 38 (1986), 263–269.

P. Chandra, Functions of classes Lp and Lip (α, p) and their Riesz means, Riv. Mat. Univ. Parma, (4) 12 (1986), 275–282.

P. Chandra, A note on degree of approximation by N¨orlund and Riesz operators, Mat. Vesn., 42 (1990), 9–10.

P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl., 275 (2002), 13–26.

E. A. Gadjieva, Investigation the Properties of Functions with Quasimnotone Fourier Coefficients in Generalized Nikolskii-Besov Spaces, (Russian), Authors Summary of Candidates Dissertation, Tbilisi (1986).

A. Guven, D. M. Israfilov, Improved inverse theorems in weighted Lebesgue and Smirnov spaces, Bull. Belg. Math. Soc., 14 (2007), 681–692.

R. Hunt, B. Muckenhoupt, R. Wheeden, Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform, Trans. Amer. Math. Soc. 176 (1973), 227–251.

D. M. Israfilov, A. Guven, Approximation by trigonometric polynomials in weighted Orlicz spaces, Stud. Math., 174 (2006), 147–168.

N. X. Ky, On approximation by trigonometric polynomials in $L_{u}^{p}$-spaces, Stud. Sci. Math. Hung., 28 (1993), 183–188.

N. X. Ky, Moduli of mean smoothness and approximation with $A_{p}$-weights, Ann. Univ. Sci. Budap., 40 (1997), 37–48.

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

R. N. Mohapatra, 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.

E. S. Quade, Trigonometric approximation in the mean, Duke Math. J., 3 (1937), 529–542.

L. Zhizhiashvili, Trigonometric Fourier Series and their Conjugates, Kluwer Academic Publishers (1996).

A. Zygmund, Trigonometric Series, Vol I, Cambridge Univ. Press, 2nd edition, (1959).

Downloads

Published

11.06.2024

How to Cite

Guven, A. (2024). Trigonometric Approximation of Functions in Weighted $\boldsymbol{L^{p}}$ Spaces. Sarajevo Journal of Mathematics, 5(1), 99–108. https://doi.org/10.5644/SJM.05.1.09

Issue

Section

Articles