Geodesic
Spaces of Smooth Functions Generated by Nonhomogeneous Differential Expressions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 89-92

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A Sobolev-type embedding theorem is established, which differs from classical statements in that the assumptions are imposed on linear combinations of the form $\sum a_j D^{\alpha_j}f_j$ with different functions $f_j$ and different multi-indices $\alpha_j$. It is applied to a classification problem for spaces of smooth functions generated by finite collections of differential expressions.
Keywords: space of smooth functions, Sobolev embedding.
Mots-clés : isomorphism 
@article{FAA_2013_47_2_a9,
     author = {S. V. Kislyakov and D. V. Maksimov and D. M. Stolyarov},
     title = {Spaces of {Smooth} {Functions} {Generated} by {Nonhomogeneous} {Differential} {Expressions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {89--92},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_2_a9/}
}
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S. V. Kislyakov; D. V. Maksimov; D. M. Stolyarov. Spaces of Smooth Functions Generated by Nonhomogeneous Differential Expressions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 89-92. http://geodesic.mathdoc.fr/item/FAA_2013_47_2_a9/