| Title:
|
A Marchaud type inequality (English) |
| Author:
|
Bustamante, Jorge |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
159-167 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a new Marchaud type inequality in $\mathbb{L}^p$ spaces. (English) |
| Keyword:
|
Marchaud type inequality |
| MSC:
|
26A15 |
| MSC:
|
26D10 |
| idZBL:
|
Zbl 07613028 |
| idMR:
|
MR4506130 |
| DOI:
|
10.14712/1213-7243.2022.014 |
| . |
| Date available:
|
2022-11-02T09:12:54Z |
| Last updated:
|
2024-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151083 |
| . |
| Reference:
|
[1] Butzer P. L., Dyckhoff H., Görlich E., Stens R. L.: Best trigonometric approximation, fractional order derivatives and Lipschitz classes.Canadian J. Math. 29 (1977), no. 4, 781–793. MR 0442566, 10.4153/CJM-1977-081-6 |
| Reference:
|
[2] Butzer P. L., Nessel R. J.: Fourier Analysis and Approximation. Volume 1: One-dimensional Theory.Pure and Applied Mathematics, 40, Academic Press, New York, 1971. MR 0510857 |
| Reference:
|
[3] DeVore R. A., Lorentz G. G.: Constructive Approximation.Grundlehren der mathematischen Wissenschaften, 303, Springer, Berlin, 1993. MR 1261635, 10.1007/978-3-662-02888-9 |
| Reference:
|
[4] Gabushin V. N.: Inequalities for the norms of a function and its derivatives in metric $L_p$-metrics.Mat. Zametki 1 (1967), 291–298 (Russian). MR 0206700 |
| Reference:
|
[5] Johnen H.: Inequalities connected with the moduli of smoothness.Mat. Vesnik 9(24) (1972), 289–303. MR 0325868 |
| Reference:
|
[6] Johnen H., Scherer K.: On the equivalence of the $K$-functional and moduli of continuity and some applications.Constructive Theory of Functions of Several Variables, Proc. Conf., Math. Res. Inst., Oberwolfach, 1976, Lecture Notes in Math., 571, Springer, Berlin, 1977, pages 119–140. MR 0487423, 10.1007/BFb0086569 |
| Reference:
|
[7] Marchaud A.: Sur les dérivées et sur les différences des fonctions de variables réelles.Thèses de l'entre-deux-guerres (1927), no. 78, 98 pages (French). MR 3532941 |
| Reference:
|
[8] Rudin W.: Functional Analysis.McGraw–Hill Series in Higher Mathematics, McGraw–Hill Book Co., New York, 1973. Zbl 0867.46001, MR 0365062 |
| Reference:
|
[9] Timan A. F.: Theory of Approximation of Functions of Real Variable.Translated from the Russian by J. Berry, English translation edited and editorial preface by J. Cossar, Pergamon Press Book International Series of Monographs in Pure and Applied Mathematics, 34, The Macmillan Company, Pergamon Press, New York, 1963. MR 0192238 |
| . |
