D. B. Bazarkhanov, “Characterizations of the Nikol'skii–Besov and Lizorkin–Triebel Function Spaces of Mixed Smoothness”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 53–65; Proc. Steklov Inst. Math., 243 (2003), 46

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 53–65 (Mi tm420)

This article is cited in 14 scientific papers (total in 14 papers)

Characterizations of the Nikol'skii–Besov and Lizorkin–Triebel Function Spaces of Mixed Smoothness

D. B. Bazarkhanov

Institute of Mathematics and Mechanics, Kazakhstan National Academy of Sciences

Full-text PDF (240 kB) Citations (14)

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Abstract: The Nikol'skii–Besov and Lizorkin–Triebel function spaces of mixed positive smoothness are characterized in terms of fairly general (including local) averages and Peetre maximal functions. Atomic decompositions for functions from these spaces are also obtained.

Received in March 2003

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: D. B. Bazarkhanov, “Characterizations of the Nikol'skii–Besov and Lizorkin–Triebel Function Spaces of Mixed Smoothness”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 53–65; Proc. Steklov Inst. Math., 243 (2003), 46–58

Citation in format AMSBIB

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\by D.~B.~Bazarkhanov

\paper Characterizations of the Nikol'skii--Besov and Lizorkin--Triebel Function Spaces of Mixed Smoothness

\inbook Function spaces, approximations, and differential equations

\bookinfo Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS

\serial Trudy Mat. Inst. Steklova

\yr 2003

\vol 243

\pages 53--65

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm420}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2049462}

\zmath{https://zbmath.org/?q=an:1090.46025}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2003

\vol 243

\pages 46--58

Linking options:

https://www.mathnet.ru/eng/tm420

https://www.mathnet.ru/eng/tm/v243/p53

This publication is cited in the following 14 articles:

D. B. Bazarkhanov, “Optimal Cubature Formulas on Classes of Periodic Functions in Several Variables”, Proc. Steklov Inst. Math., 312 (2021), 16–36
Van Kien Nguyen, “Gelfand Numbers of Embeddings of Mixed Besov Spaces”, J. Complex., 41 (2017), 35–57
Van Kien Nguyen, “Weyl and Bernstein numbers of embeddings of Sobolev spaces with dominating mixed smoothness”, J. Complex., 36 (2016), 46–73
Van Kien Nguyen, Sickel W., “Weyl Numbers of Embeddings of Tensor Product Besov Spaces”, J. Approx. Theory, 200 (2015), 170–220
Van Kien Nguyen, “Bernstein Numbers of Embeddings of Isotropic and Dominating Mixed Besov Spaces”, Math. Nachr., 288:14-15 (2015), 1694–1717
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
Ullrich T., “Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits”, J. Funct. Space Appl., 2012, 163213
Rauhut H., Ullrich T., “Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type”, J Funct Anal, 260:11 (2011), 3299–3362
D. B. Bazarkhanov, “Estimates of the Fourier Widths of Classes of Nikolskii–Besov and Lizorkin–Triebel Types of Periodic Functions of Several Variables”, Math. Notes, 87:2 (2010), 281–284
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
A. I. Parfenov, “A criterion for straightening a Lipschitz surface in the Lizorkin–Triebel sense. III”, Siberian Adv. Math., 21:2 (2011), 100–129
Hansen M., Vybiral J., “The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness”, Georgian Mathematical Journal, 16:4 (2009), 667–682
Vybiral J., Sickel W., “Traces of functions with a dominating mixed derivative in R–3”, Czechoslovak Mathematical Journal, 57:4 (2007), 1239–1273
D. B. Bazarkhanov, “Equivalent (Quasi)Norms for Certain Function Spaces of Generalized Mixed Smoothness”, Proc. Steklov Inst. Math., 248 (2005), 21–34

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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