Literature cited
P. I. Lizorkin and S. M. Nikol'skii, “Classification of differentiable functions on the basis of the spaces with dominating mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR,77, 143–167 (1965).
S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag (1974).
Yu. A. Brychkov, “On the theory of the spacesS rp L (R n ),” Dokl. Akad. Nauk SSSR,219, No. 6, 1289–1290 (1974).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock (1961).
P. I. Lizorkin, “The generalized Liouville differentiation and the function spacesL rp (R n ). Imbedding theorems,” Mat. Sb.,60, No. 3, 325–353 (1963).
Yu. A. Brychkov, “On the order of singularity of generalized functions with respect to a part of the variables,” Dokl. Akad. Nauk SSSR,205, No. 2, 271–273 (1972).
Yu. A. Brychkov, “On the smoothness with respect to a part of the variables of the solutions of linear partial differential equations,” Differents. Uravn.,10, No. 2, 281–289 (1974).
A. Benedek and R. Panzone, “The spaces Lp with mixed norm,” Duke Math. J.,28, No. 3, 301–324 (1961).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 31, No. 5, pp. 679–694, May, 1982.
Rights and permissions
About this article
Cite this article
Brychkov, Y.A. Theory of spaces with dominating mixed derivative. Mathematical Notes of the Academy of Sciences of the USSR 31, 345–354 (1982). https://doi.org/10.1007/BF01145711
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01145711