On Smoothness in $L_p$, $0 p 1$
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 97-104.

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

We discuss properties of functions which are covered by spreading the differentiation operator from the space $W_1^1$.
Keywords: differentiation operator
Mots-clés : quasinorm.
@article{MAIS_2012_19_3_a5,
     author = {A. N. Morozov},
     title = {On {Smoothness} in $L_p$, $0 < p < 1$},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {97--104},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a5/}
}
TY  - JOUR
AU  - A. N. Morozov
TI  - On Smoothness in $L_p$, $0 < p < 1$
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2012
SP  - 97
EP  - 104
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a5/
LA  - ru
ID  - MAIS_2012_19_3_a5
ER  - 
%0 Journal Article
%A A. N. Morozov
%T On Smoothness in $L_p$, $0 < p < 1$
%J Modelirovanie i analiz informacionnyh sistem
%D 2012
%P 97-104
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a5/
%G ru
%F MAIS_2012_19_3_a5
A. N. Morozov. On Smoothness in $L_p$, $0 < p < 1$. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 97-104. http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a5/

[1] A. N. Morozov, “Kusochno-polinomialnye priblizheniya i differentsiruemost v prostranstvakh $L_p$ ($0

1$)”, Model. i analiz inform. sistem, 12:1 (2005), 18–21

[2] A. N. Morozov, “Operatory differentsirovaniya v prostranstvakh $L_p$”, Matematika, kibernetika, informatika, Trudy mezhdunarodnoi nauchnoi konferentsii, posvyaschennoi pamyati professora A. Yu. Levina (25–26 iyunya 2008 g., Yaroslavl), Yaroslavl, 2008, 196 pp.

[3] A. N. Morozov, “Opisanie prostranstv differentsiruemykh funktsii pri pomoschi lokalnykh priblizhenii”, Model. i analiz inform. sistem, 16:1 (2009), 7–15

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

[5] E. A. Storozhenko, V. G. Krotov, P. Osvald, “Pryamye i obratnye teoremy tipa Dzheksona v prostranstvakh $L_p$, $0

1$”, Matem. sb., 98:3 (1975), 395–415 | MR | Zbl

[6] Z. Ditzian, V. H. Hristov, K. G. Ivanov, “Moduli of Smoothness and K-Functionals in $L_p$, $0

1$”, Constr. Approx., 11 (1995), 67–83 | DOI | MR | Zbl

[7] Z. Ditzian, “Polynomial Approximation and $w_{\varphi}^r(f,t)$ Twenty Years Later”, Surveys in Appr. Theory, 3 (2007), 106–151 | MR | Zbl

[8] K. V. Runovskii, Priblizhenie semeistvami lineinykh polinomialnykh operatorov, Avtoref. dis. $\dots$ d-ra fiz.-mat. nauk, M., 2010 http://mech.math.msu.su/~snark/files/vak/aro8.pdf

[9] A. N. Morozov, “Ob operatorakh differentsirovaniya i integrirovaniya”, Model. i analiz inform. sistem, 18:3 (2011), 50–57

[10] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, Nauka, M., 1984, 750 pp. | MR | Zbl

[11] I. Berg, I. Lefstrem, Interpolyatsionnye prostranstva. Vvedenie, per. s angl. V. S. Kryuchkova, P. I. Lizorkina, Mir, M., 1980, 264 pp. | MR