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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 2, Pages 89–92
DOI: https://doi.org/10.4213/faa3114 (Mi faa3114) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Spaces of Smooth Functions Generated by Nonhomogeneous Differential Expressions

S. V. Kislyakova, D. V. Maksimovb, D. M. Stolyarovc

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Saint-Petersburg State Polytechnical University
c Saint-Petersburg State University
Full-text PDF (157 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa3114
Abstract: A Sobolev-type embedding theorem is established, which differs from classical statements in that the assumptions are imposed on linear combinations of the form ∑ajDαjfj with different functions fj and different multi-indices αj. It is applied to a classification problem for spaces of smooth functions generated by finite collections of differential expressions.
Keywords: space of smooth functions, isomorphism, Sobolev embedding.
Received: 01.08.2012
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 2, Pages 157–159
DOI: https://doi.org/10.1007/s10688-013-0021-0
Bibliographic databases:
Document Type: Article
UDC: 517.982
Language: Russian
Citation: S. V. Kislyakov, D. V. Maksimov, D. M. Stolyarov, “Spaces of Smooth Functions Generated by Nonhomogeneous Differential Expressions”, Funktsional. Anal. i Prilozhen., 47:2 (2013), 89–92; Funct. Anal. Appl., 47:2 (2013), 157–159
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3114
  • https://www.mathnet.ru/eng/faa/v47/i2/p89
    • This publication is cited in the following 4 articles:
    1. Krystian Kazaniecki, Dmitriy M. Stolyarov, Michał Wojciechowski, “Anisotropic Ornstein noninequalities”, Anal. PDE, 10:2 (2017), 351  crossref
    2. S.V. Kislyakov, D.V. Maksimov, D.M. Stolyarov, “Differential expressions with mixed homogeneity and spaces of smooth functions they generate in arbitrary dimension”, Journal of Functional Analysis, 269:10 (2015), 3220  crossref
    3. D. M. Stolyarov, “Bilinear embedding theorems for differential operators in $\mathbb R^2$”, J. Math. Sci. (N. Y.), 209:5 (2015), 792–807  mathnet  crossref  mathscinet
    4. D. M. Stolyarov, M. Wojciechowski, “Dimension of gradient measures”, C. R. Math. Acad. Sci. Paris, 352:10 (2014), 791–795  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:78
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