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Tr. Mat. Inst. Steklova, 2005, Volume 248, Pages 26–39 (Mi tm115)  

This article is cited in 8 scientific papers (total in 8 papers)

Equivalent (Quasi)Norms for Certain Function Spaces of Generalized Mixed Smoothness

D. B. Bazarkhanov

Institute of Mathematics and Mechanics, Kazakhstan National Academy of Sciences

Abstract: For certain (quasi)Banach function spaces of generalized mixed positive smoothness defined by (mixed) weighted norms of smooth dyadic decompositions of their Fourier transforms, characterizations are obtained in terms of rather general averages, their Peetre maximal functions, atomic and molecular representations, as well as in terms of the so-called $\varphi$-transforms.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 248, 21–34

Bibliographic databases:

UDC: 517.518
Received in October 2004

Citation: D. B. Bazarkhanov, “Equivalent (Quasi)Norms for Certain Function Spaces of Generalized Mixed Smoothness”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 248, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 26–39; Proc. Steklov Inst. Math., 248 (2005), 21–34

Citation in format AMSBIB
\Bibitem{Baz05}
\by D.~B.~Bazarkhanov
\paper Equivalent (Quasi)Norms for Certain Function Spaces of Generalized Mixed Smoothness
\inbook Studies on function theory and differential equations
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 248
\pages 26--39
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm115}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2165912}
\zmath{https://zbmath.org/?q=an:1129.46023}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 248
\pages 21--34


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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. B. Bazarkhanov, “Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I”, Proc. Steklov Inst. Math., 269 (2010), 2–24  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. A. I. Parfenov, “A criterion for straightening a Lipschitz surface in the Lizorkin–Triebel sense. III”, Siberian Adv. Math., 21:2 (2011), 100–129  mathnet  crossref  mathscinet
    3. Sickel W., Ullrich T., “Spline interpolation on sparse grids”, Appl Anal, 90:3–4 (2011), 337–383  crossref  mathscinet  zmath  isi  elib  scopus
    4. Hansen M., Sickel W., “Best M-Term Approximation and Sobolev-Besov Spaces of Dominating Mixed Smoothness-the Case of Compact Embeddings”, Constr. Approx., 36:1 (2012), 1–51  crossref  mathscinet  zmath  isi  elib  scopus
    5. Van Kien Nguyen Sickel W., “Weyl Numbers of Embeddings of Tensor Product Besov Spaces”, J. Approx. Theory, 200 (2015), 170–220  crossref  mathscinet  zmath  isi  scopus
    6. Van Kien Nguyen, “Bernstein Numbers of Embeddings of Isotropic and Dominating Mixed Besov Spaces”, Math. Nachr., 288:14-15 (2015), 1694–1717  crossref  mathscinet  zmath  isi  scopus
    7. Van Kien Nguyen, “Weyl and Bernstein numbers of embeddings of Sobolev spaces with dominating mixed smoothness”, J. Complex., 36 (2016), 46–73  crossref  mathscinet  zmath  isi  scopus
    8. Van Kien Nguyen, “Gelfand Numbers of Embeddings of Mixed Besov Spaces”, J. Complex., 41 (2017), 35–57  crossref  mathscinet  zmath  isi  scopus
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