Ukrainian Mathematical Journal

, Volume 70, IssueÂ 8, pp 1319â€“1325

# Approximation of Periodic Functions of Many Variables by Functions of a Smaller Number of Variables in Orlicz Metric Spaces

• Yu.Â A.Â Babich
• T.Â F.Â Mikhailova
Brief Communications

For periodic functions of many variables, we propose a method for their approximation in the Orlicz spaces L(đť•‹m). According to this method, the functions are approximated by the sums of functions of smaller number of variables each of which is piecewise-constant in one variable for fixed values of the other variables. A Jackson-type inequality is analyzed for these approximations in terms of the mixed module of continuity.

## References

1. 1.
S. A. Pichugov, â€śYoung constants of the space L p ,â€ť Mat. Zametki, 43, No. 5, 604â€“614 (1988).
2. 2.
I. M. Vinogradov, Foundations of the Number Theory [in Russian], Nauka, Moscow (1981).Google Scholar
3. 3.
K. V. Runovskii, â€śOn the approximation of a family of linear polynomial operators in the spaces L p , 0 < p < 1,â€ť Mat. Sb., 185, No. 8, 81â€“102 (1994).Google Scholar
4. 4.
S. A. Pichugov, â€śOn the Jackson theorem for periodic functions in spaces with integral metric,â€ť Ukr. Mat. Zh., 52, No. 1, 122â€“133 (2000); English translation: Ukr. Math. J., 52, No. 1, 133â€“147 (2000).Google Scholar
5. 5.
S. A. Pichugov, â€śOn the Jackson theorem for periodic functions in metric spaces with integral metric. II,â€ť Ukr. Mat. Zh., 63, No. 11, 1524â€“1533 (2011); English translation: Ukr. Math. J., 63, No. 11, 1733â€“1744 (2012).Google Scholar
6. 6.
S. A. Pichugov, â€śApproximation of periodic functions by constants in the metric spaces Ď†(L),â€ť Ukr. Mat. Zh., 46, No. 8, 1095â€“1098 (1994); English translation: Ukr. Math. J., 46, No. 8, 1206â€“1209 (1994).Google Scholar
7. 7.
S. A. Pichugov, â€śSmoothness of functions in the metric spaces L đťś“ ,â€ť Ukr. Mat. Zh., 64, No. 9, 1214â€“1232 (2012); English translation: Ukr. Math. J., 64, No. 9, 1382â€“1402 (2013).Google Scholar

## Authors and Affiliations

• Yu.Â A.Â Babich
• 1
• T.Â F.Â Mikhailova
• 1
1. 1.Dnepropetrovsk National University of Railway TransportDniproUkraine