Geodesic
The Correction Theorem for Anisotropic Spaces
Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 323-333.

Voir la notice de l'article provenant de la source Math-Net.Ru

The following old problem is solved. Given an $\varepsilon>0$, a function $f \colon [0,1]^n\to\mathbb R$, and the partial moduli of continuity of this function evaluated in a symmetric space $X$, find a set $I(\varepsilon)$ of measure larger than $1-\varepsilon$ such that the partial uniform moduli of continuity of f determined for the points of this set admit an unimprovable (with respect to all restrictions to sets of measure larger than $1-\varepsilon$) estimate of partial uniform moduli of continuity and write out this estimate of the uniform partial moduli of continuity. 
@article{MZM_2001_70_3_a0,
     author = {E. I. Berezhnoi},
     title = {The {Correction} {Theorem} for {Anisotropic} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--333},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a0/}
}
TY  - JOUR
AU  - E. I. Berezhnoi
TI  - The Correction Theorem for Anisotropic Spaces
JO  - Matematičeskie zametki
PY  - 2001
SP  - 323
EP  - 333
VL  - 70
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a0/
LA  - ru
ID  - MZM_2001_70_3_a0
ER  - 
%0 Journal Article
%A E. I. Berezhnoi
%T The Correction Theorem for Anisotropic Spaces
%J Matematičeskie zametki
%D 2001
%P 323-333
%V 70
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a0/
%G ru
%F MZM_2001_70_3_a0
E. I. Berezhnoi. The Correction Theorem for Anisotropic Spaces. Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a0/

[1] Zigmund A., Trigonometricheskie ryady, T. 1, 2, Mir, M., 1965

[2] Berezhnoi E. I., “Otsenki ravnomernogo modulya nepreryvnosti funktsii iz simmetrichnykh prostranstv”, Izv. RAN, 60:2 (1996), 3–20 | MR | Zbl

[3] Brudnyi Yu. A., “Prostranstva, opredelyaemye s pomoschyu lokalnykh priblizhenii”, Tr. MMO, 24, URSS, M., 1971, 69–132 | MR | Zbl

[4] Kolyada V. I., “Otsenki maksimalnykh funktsii, svyazannykh s lokalnoi gladkostyu”, Dokl. AN SSSR, 293 (1987), 534–537 | MR | Zbl

[5] Oskolkov K. I., “Ravnomernyi modul nepreryvnosti summiruemykh funktsii na mnozhestvakh polozhitelnoi mery”, Dokl. AN SSSR, 229:2 (1976), 304–306 | MR | Zbl

[6] Ulyanov P. L., “O rabotakh N. N. Luzina po metricheskoi teorii funktsii”, UMN, 40:3 (1985), 15–70 | MR | Zbl

[7] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1977

[8] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1977 | Zbl

[9] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974