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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 244–256 (Mi tm432)  
This article is cited in 6 scientific papers (total in 6 papers)

On the Besov and Besov–Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives

M. K. Potapova, B. V. Simonovb, S. Yu. Tikhonova

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Volgograd State Technical University
Full-text PDF (223 kB) Citations (6)
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Abstract: Fractional-order derivatives in the sense of Weyl are considered for functions of several variables. Estimates for the mixed moduli of smoothness for these derivatives are obtained in terms of the mixed moduli of smoothness of the functions themselves. These estimates are applied to study the interrelation between the Besov and Nikol'skii–Besov classes and the other classes of functions.
Received in April 2003
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “On the Besov and Besov–Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives”, 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, 244–256; Proc. Steklov Inst. Math., 243 (2003), 234–246
Citation in format AMSBIB
\Bibitem{PotSimTik03}
\by M.~K.~Potapov, B.~V.~Simonov, S.~Yu.~Tikhonov
\paper On the Besov and Besov--Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives
\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 244--256
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm432}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2054437}
\zmath{https://zbmath.org/?q=an:1089.46024}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 243
\pages 234--246
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    • This publication is cited in the following 6 articles:
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