Geodesic
Dyadic Nikolskii–Besov Spaces and Their Relationship to Classical Spaces
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 683-695

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Properties of dyadic spaces are considered and a relationship between dyadic and classical spaces is described. A property of classical spaces is proved by using the technique of dyadic spaces.
Mots-clés : dyadic Nikolskii–Besov spaces, quasicube
Keywords: local approximation, approximation space, smooth spline function, Bessel potential spaces. 
I. P. Irodova. Dyadic Nikolskii–Besov Spaces and Their Relationship to Classical Spaces. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 683-695. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a4/
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[1] I. P. Irodova, “O nekotorykh svoistvakh diadicheskikh prostranstv Besova”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy matematicheskogo obrazovaniya, t. 1, Trudy mezhdunar. konf. un-ta druzhby narodov, Ros. un-t druzhby narodov, M., 1998, 78–81

[2] I. P. Irodova, “Svoistva funktsii, zadannykh skorostyu ubyvaniya kusochno-polinomialnoi approksimatsii”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, YarGU, Yaroslavl, 1980, 92–117 | MR | Zbl

[3] R. A. Devore, V. A. Popov, “Interpolation of Besov Spaces”, Trans. Amer. Math. Soc., 305:1 (1988), 397–414 | DOI | MR | Zbl

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

[5] E. A. Ctorozhenko, P. Osvald, “Teoremy Dzheksona v prostranstvakh $L_p$, $0

1$”, Sib. matem. zhurn., 19:4 (1978), 888–901 | MR | Zbl

[6] I. P. Irodova, “Diadicheskie prostranstva Besova”, Algebra i analiz, 12:3 (2000), 40–80 | MR | Zbl

[7] J. Peetre, G. Sparr, “Interpolation of normed Abelian groups”, Ann. Mat. Pura Appl. (4), 92 (1972), 217–262 | DOI | MR | Zbl

[8] Yu. A. Brudnyi, I. P. Irodova, “Nelineinaya splain-approksimatsiya i $B$-prostranstva”, Trudy Mezhdunarodnoi konferentsii po teorii priblizhenii (Kiev, 1983), Nauka, M., 1987, 71–75

[9] R. A. DeVore, B. Javerth, V. A. Popov, “Compression of wavelet decompositions”, Amer. J. Math., 114:4 (1992), 737–785 | DOI | MR | Zbl

[10] I. P. Irodova, “Diadicheskie i klassicheskie prostranstva Besova”, Matematika. Materialy vserossiiskoi nauchnoi konferentsii, YarGU, Yaroslavl, 2003, 257–264

[11] I. P. Irodova, “Obobschenie neravenstva Marsho”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, YarGU, Yaroslavl, 1984, 63–69 | MR | Zbl

[12] L. D. Kydryavtsev, S. M. Nikolskii, “Prostranstva differentsiruemykh funktsii mnogikh peremennykh i teoremy vlozheniya”, Itogi nauki i tekhniki. Sovrem. problemy matem. Fundam. napr., 26, VINITI, M., 1988, 5–157 | MR | Zbl

[13] J. R. Dorronsoro, “A characterization of Potential Spaces”, Amer. Math. Soc., 95:1 (1985), 21–31 | DOI | MR | Zbl