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 Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 78–94 (Mi timm1231)

Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness

Sh. A. Balgimbaeva, T. I. Smirnov

Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan

Abstract: Order-exact bounds are obtained for Fourier widths of the Nikol'skii-Besov classes $\mathrm{SB}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ and Triebel-Lizorkin classes $\mathrm{SF}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ of functions with a given majorant $\Omega$ for the mixed modulus of smoothness of order $l$ in the space $L_q(\mathbb{T}^d)$ for all relations between the parameters $p$, $q$, and $\theta$ under some conditions on $\Omega$. The upper bounds follow from order-exact bounds for approximations of the classes $\mathrm{SB}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ and $\mathrm{SF}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ by special partial sums of Fourier series in the multiple system $\Psi_d$ of periodized Meyer wavelets.

Keywords: fourier width, mixed modulus of smoothness, function spaces, wavelet system.

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Bibliographic databases:
UDC: 517.5

Citation: Sh. A. Balgimbaeva, T. I. Smirnov, “Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 78–94

Citation in format AMSBIB
\Bibitem{BalSmi15} \by Sh.~A.~Balgimbaeva, T.~I.~Smirnov \paper Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2015 \vol 21 \issue 4 \pages 78--94 \mathnet{http://mi.mathnet.ru/timm1231} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468432} \elib{https://elibrary.ru/item.asp?id=25300987} 

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This publication is cited in the following articles:
1. Sh. A. Balgimbayeva, T. I. Smirnov, “Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness”, Siberian Math. J., 59:2 (2018), 217–230
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