Abstract
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.
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I. P. Irodova, “On some properties of dyadic Besov spaces,” in Functional Spaces. Differential Operators. Problems of Mathematical Education, Proceedings of the International Conference at Peoples’ Friendship University, Moscow, Russia, 1988 (Ross. Univ. Druzhby Narodov, Moscow, 1998), Vol. 1, pp. 78–81.
I. P. Irodova, “Properties of functions determined by the rate of decrease of piecewise polynomial approximation,” in Studies in the Theory of Functions of Several Real Variables (Yaroslavskii Gos. Univ., Yaroslavl, 1980), pp. 92–117 [in Russian].
R. A. Devore and V. A. Popov, “Interpolation of Besov spaces,” Trans. Amer. Math. Soc. 305(1), 397–414 (1988).
Yu. A. Brudnyi, “Spaces defined by using local approximations,” Tr. Mosk. Mat. O-va 24, 69–132 (1971).
É. A. Storozhenko and P. Osval’d [P. Oswald], “Jackson’s theorems in the spaces L p, 0 < p < 1,” Sibirsk. Mat. Zh. 19(4), 888–901 (1978).
I. P. Irodova, “Dyadic Besov spaces,” Algebra Anal. 12(3), 40–80 (2000) [St. Petersbg. Math. J. 12 (3), 379–405 (2001)].
J. Peetre and G. Sparr, “Interpolation of normed Abelian groups,” Ann. Mat. Pura Appl. (4) 92, 217–262 (1972).
Yu. A. Brudnyi and I. P. Irodova, “Nonlinear spline-approximation and B-spaces,” in Proceedings of International Conference on Approximation Theory, Kiev, Ukraina, 1983 (Nauka, Moscow, 1987), pp. 71–75.
R. A. DeVore, B. Javerth and V. A. Popov, “Compression of wavelet decompositions,” Amer. J. Math. 114(4), 737–785 (1992).
I. P. Irodova, “Dyadic and classical Besov spaces,” in Proceedings of the All-Russia Scientific Conference “Mathematics,” Yaroslavl, Russia, 2003 (Yaroslavskii Gos. Univ., Yaroslavl, 2003), pp. 257–264.
I. P. Irodova, “Generalization of the Marchaud inequality,” in Studies in the Theory of Functions of Several Real Variables (Yaroslavskii Gos. Univ., Yaroslavl, 1984), pp. 63–69 [in Russian].
L. D. Kudryavtsev and S. M. Nikol’skii, “Spaces of differentiable functions of several variables and embedding theorems,” in [Encyclopaedia of Mathematical Sciences, Vol. 26: Analysis. III (Springer-Verlag, Berlin, 1991), pp. 1–140].
J. R. Dorronsoro, “A characterization of potential spaces,” Amer. Math. Soc. 95(1), 21–31 (1985).
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Original Russian Text © I. P. Irodova, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 5, pp. 683–695.
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Irodova, I.P. Dyadic Nikol’skii-Besov spaces and their relationship to classical spaces. Math Notes 83, 624–634 (2008). https://doi.org/10.1134/S0001434608050052
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DOI: https://doi.org/10.1134/S0001434608050052