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Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 8, Pages 83–86 (Mi ivm3059)  

Brief communications

The embedding and approximation of classes of functions with a dominant mixed difference

M. B. Sikhov

Chair of Functional Analysis and Probability Theory, Kazakh National University, Almaty, Republic of Kazakhastan

Abstract: We obtain a criterion for embedding the class $SH_p^\Omega$ into that $SB_{q,\theta}^{\Omega^*}$ ($1<p\leq q<\infty$). We also determine the exact order of the best approximations of functions from classes $SB_{p,\theta}^\Omega$ by trigonometric polynomials whose harmonics belong to sets generated by level surfaces of the majorant $\Lambda(t)$.

Keywords: Besov's spases, embedding theorem, modulus of continuity, best approximations.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:8, 69–71

Bibliographic databases:

UDC: 517.518
Received: 20.12.2008

Citation: M. B. Sikhov, “The embedding and approximation of classes of functions with a dominant mixed difference”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 8, 83–86; Russian Math. (Iz. VUZ), 53:8 (2009), 69–71

Citation in format AMSBIB
\Bibitem{Sik09}
\by M.~B.~Sikhov
\paper The embedding and approximation of classes of functions with a~dominant mixed difference
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 8
\pages 83--86
\mathnet{http://mi.mathnet.ru/ivm3059}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2584262}
\zmath{https://zbmath.org/?q=an:1182.46024}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 8
\pages 69--71
\crossref{https://doi.org/10.3103/S1066369X09080118}


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