Geodesic
Function Spaces of Lizorkin–Triebel Type on an Irregular Domain
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 32-43 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

On an irregular domain $G\subset\mathbb R^n$ of a certain type, we introduce function spaces of fractional smoothness $s>0$ that are similar to the Lizorkin–Triebel spaces. We prove embedding theorems that show how these spaces are related to the Sobolev and Lebesgue spaces $W_p^m(G)$ and $L_p(G)$. 
@article{TM_2008_260_a2,
     author = {O. V. Besov},
     title = {Function {Spaces} of {Lizorkin{\textendash}Triebel} {Type} on an {Irregular} {Domain}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {32--43},
     year = {2008},
     volume = {260},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a2/}
}
TY  - JOUR
AU  - O. V. Besov
TI  - Function Spaces of Lizorkin–Triebel Type on an Irregular Domain
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2008
SP  - 32
EP  - 43
VL  - 260
UR  - http://geodesic.mathdoc.fr/item/TM_2008_260_a2/
LA  - ru
ID  - TM_2008_260_a2
ER  - 
%0 Journal Article
%A O. V. Besov
%T Function Spaces of Lizorkin–Triebel Type on an Irregular Domain
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2008
%P 32-43
%V 260
%U http://geodesic.mathdoc.fr/item/TM_2008_260_a2/
%G ru
%F TM_2008_260_a2
O. V. Besov. Function Spaces of Lizorkin–Triebel Type on an Irregular Domain. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 32-43. http://geodesic.mathdoc.fr/item/TM_2008_260_a2/

[1] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[2] Mazya V. G., Prostranstva S. L. Soboleva, Izd-vo LGU, L., 1985 | MR

[3] Reshetnyak Yu. G., “Integralnye predstavleniya differentsiruemykh funktsii v oblastyakh s negladkoi granitsei”, Sib. mat. zhurn., 21:6 (1980), 108–116 | MR | Zbl

[4] Goldshtein V. M., Reshetnyak Yu. G., Vvedenie v teoriyu funktsii s obobschennymi proizvodnymi i kvazikonformnye otobrazheniya, Nauka, M., 1983 | MR

[5] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1996 | MR

[6] Besov O. V., “Teorema vlozheniya Soboleva dlya oblasti s neregulyarnoi granitsei”, Mat. sb., 192:3 (2001), 3–26 | MR | Zbl

[7] Kilpeläinen T., Malý J., “Sobolev inequalities on sets with irregular boundaries”, Ztschr. Anal. und Anwend., 19:2 (2000), 369–380 | MR | Zbl

[8] Labutin D. A., “Neuluchshaemost neravenstv Soboleva dlya klassa neregulyarnykh oblastei”, Tr. MIAN., 232, Nauka, M., 2001, 218–222 | MR | Zbl

[9] Besov O. V., “Prostranstva funktsii drobnoi gladkosti na neregulyarnoi oblasti”, Mat. zametki, 74:2 (2003), 163–183 | MR | Zbl

[10] Besov O. V., “Ekvivalentnye normy v prostranstvakh funktsii drobnoi gladkosti na proizvolnoi oblasti”, Mat. zametki, 74:3 (2003), 340–349 | MR | Zbl

[11] Besov O. V., “O kompaktnosti vlozhenii vesovykh prostranstv Soboleva na oblasti s neregulyarnoi granitsei”, Tr. MIAN, 232, Nauka, M., 2001, 72–93 | MR | Zbl