that was developed by the author in previous papers. In particular, a direct theorem and an inverse theorem on approximation 'by angle' of trigonometric polynomials are proved in the case of higher-order moduli of smoothness.
@article{SM_1995_82_2_a11,
author = {K. V. Runovskii},
title = {On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$},
journal = {Sbornik. Mathematics},
pages = {441--459},
year = {1995},
volume = {82},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1995_82_2_a11/}
}
K. V. Runovskii. On approximation by families of linear polynomial operators in $l_P$-spaces, $0
[1] Stechkin S. B., “O poryadke nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR. Ser. matem., 5:3 (1951), 219–242
[2] Potapov M. K., “O priblizhenii “uglom””, Tr. konf. po konstr. teorii funktsii (Budapesht), 1972, 371–399 | MR | Zbl
[3] Storozhenko E. A., Krotov V. G., Osvald P., “Pryamye i obratnye teoremy tipa Dzheksona v prostranstvakh $L_p$, $0
1$”, Matem. sb., 98(140) (1975), 395–415 | MR | Zbl[4] Storozhenko E. A., Osvald P., “Teorema Dzheksona v prostranstvakh $L_p(\mathbb R^k)$, $0
\nobreak 1$”, Sib. matem. zhurn., 19:4 (1978), 888–901 | MR | Zbl[5] Runovskii K. V., “Pryamaya teorema o priblizhenii “uglom” v prostranstvakh $L_p$, $0
1$”, Matem. zametki, 52:5 (1992), 93–96 | MR | Zbl[6] Runovskii K. V., “O semeistvakh lineinykh polinomialnykh operatorov v prostranstvakh $L_p$, $0
1$”, Matem. sb., 184:2 (1993), 33–42 | Zbl[7] Stechkin S. B., “Obobschenie nekotorykh neravenstv S. N. Bernshteina”, DAN SSSR, 60:9 (1948), 1511–1514 | MR | Zbl
[8] Aristov V. V., “O neravenstvakh S. N. Bernshteina dlya algebraicheskikh i trigonometricheskikh polinomov”, DAN SSSR, 246:6 (1979), 1289–1292 | MR
[9] Storozhenko E. A., “Priblizhenie funktsii interpolyatsionnymi v srednem splainami”, Izv. vuzov. Matematika, 1976, no. 12, 82–95 | Zbl
[10] Runovskii K. V., “Ob odnoi otsenke dlya integralnogo modulya gladkosti”, Izv. vuzov. Matematika, 1992, no. 1, 78–80 | MR | Zbl