Geodesic
Equivalent quasi-norms involving differences and moduli of continuity in anisotropic Nikol’skii--Besov spaces
Eurasian mathematical journal, Tome 7 (2016) no. 2, pp. 7-18.

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In this paper we study the equivalence of quasi-norms in the anisotropic Nikol’skii–Besov $B_{p,\theta}^l(\mathbb{R}^n)$ spaces involving differences and moduli of continuity for $0$. 
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B. Halim; A. Senouci. Equivalent quasi-norms involving differences and moduli of continuity in anisotropic Nikol’skii--Besov spaces. Eurasian mathematical journal, Tome 7 (2016) no. 2, pp. 7-18. http://geodesic.mathdoc.fr/item/EMJ_2016_7_2_a0/

[1] N. Azzouz, V. I. Burenkov, A. Senouci, “A weighted Hardy-type inequality for $0 p 1$ with sharp constant”, Mathematical inequalities and Applications, 18:2 (2015), 787–799 | DOI | MR | Zbl

[2] O. V. Besov, V. P. IL'in, S. M. Nikol'skii, Integral representations of functions and embedding theorems, 1st Edition, Nauka, M., 1975 (in Russian) ; 2nd Edition, Nauka, M., 1996 (in Russian); English transl.: v. 1, 2, 1st edition, Wiley, Chichester, 1979 | MR | Zbl | Zbl

[3] V. I. Burenkov, A. Senouci, T. V. Tararykova, “Equivalent quasi-norms involving differences and moduli of continuity”, Journal of complex variables and elliptic equations, 55:8–10 (2010), 759–769 | DOI | MR | Zbl

[4] V. I. Burenkov, Sobolev spaces on domains, B. G. Teubner, Stuttgart–Leipzig, 1997 | MR

[5] V. I. Burenkov, M. L. Goldman, Solutions of exercises on the topics: generalized Minkowski's inequality. Hardy's inequality, Peoples' Freindship University of Russia, M., 1990 (in Russian)

[6] S. M. Nikol'skii, Approximation of functions of several variables and embedding theorems, 1st Edition, Nauka, M., 1969 (Russian) ; 2nd Edition, Nauka, M., 1977 (Russian); English Transl.: 1st Edition, Springer, Berlin, 1975 | MR

[7] A. Senouci, T. V. Tararykova, “Hardy-type inequality for $0 p 1$”, Evraziiskii Matematicheskii Zhurnal, 2 (2008), 111–116

[8] H. Triebel, Theory of functions spaces, v. II, Birkhäuser, Basel–Boston–Stuttgart, 1992 | MR