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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 2, Pages 89–92 (Mi faa3114)  

This article is cited in 2 scientific papers (total in 2 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

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 $\sum a_j D^{\alpha_j}f_j$ 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, isomorphism, Sobolev embedding

DOI: https://doi.org/10.4213/faa3114

Full text: PDF file (157 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:2, 157–159

Bibliographic databases:

UDC: 517.982
Received: 01.08.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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