Abstract
The embedding of the anisotropic spaces \(B_{p_1 , \ldots ,p_n ,\theta }^{\omega _1 , \ldots ,\omega _n } \left( {\mathbb{R}^n } \right)\) with mixed norm is studied. We establish some necessary and sufficient conditions of the embedding \(B_{p_1 , \ldots ,p_n ,\theta }^{\omega _1 , \ldots ,\omega _n } \left( {\mathbb{R}^n } \right) \subset L^{q_1 , \ldots ,q_n } \left( {\mathbb{R}^n } \right)\).
Similar content being viewed by others
References
Gol’dman N. A., “Imbedding theorems for anisotropic Nikol’skiĭ-Besov spaces with moduli of continuity of a general type,” Proc. Steklov Inst. Math., 170, 95–116 (1987).
Kolyada V. I., “The embedding of certain classes of functions of several variables,” Siberian Math. J., 14, No. 4, 530–546 (1973).
Kolyada V. I., “Rearrangements of functions and embedding theorems,” Russian Math. Surveys, 44, No. 5, 73–117 (1989).
Nikol’skiĭ S. M., Approximation of Functions in Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).
Besov O. V., Il’in V. P., and Nikol’skiĭ S. M., Integral Representations of Functions and Embedding Theorems, John Wiley and Sons, New York etc. (1978).
Gol’dman N. A., “The method of coverings for description of general spaces of Besov type,” Proc. Steklov Inst. Math., 156, 51–87 (1983).
Envelopes and Sharp Embeddings of Function Spaces, Chapman & Hall/CRC, Boca Raton, FL (2007) (Chapman & Hall/CRC Res. Notes Math.; V. 437).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2014 Suleimenov K. and Tashatov N.N.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 2, pp. 436–453, March–April, 2014.
Rights and permissions
About this article
Cite this article
Suleimenov, K., Tashatov, N.N. On the embedding of anisotropic Nikol’skiĭ-Besov mixed norm spaces. Sib Math J 55, 356–371 (2014). https://doi.org/10.1134/S0037446614020189
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446614020189