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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 3, Pages 295–304 (Mi isu513)  

Mathematics

Approximation of Functions by Fourier–Haar Sums in Weighted Variable Lebesgue and Sobolev Spaces

M. G. Magomed-Kasumov

Daghestan Scientific Centre of Russian Academy of Sciences, 45, Gadgieva str., Makhachkala, Republic of Dagestan, 367000, Russia

Abstract: It is considered weighted variable Lebesgue $L^{p(x)}_w$ and Sobolev $W_{p(\cdot),w}$ spaces with conditions on exponent $p(x) \ge 1$ and weight $w(x)$ that provide Haar system to be a basis in $L^{p(x)}_w$. In such spaces there were obtained estimates of Fourier–Haar sums convergence speed. Estimates are given in terms of modulus of continuity $\Omega(f,\delta)_{p(\cdot),w}$, based on mean shift (Steklov's function).

Key words: weighted space, Lebesgue space, Sobolev space, variable exponent, modulus of continuity, Steklov's function, direct theorems of approximation theory, convergence speed, Fourier–Haar sums, Muckenhoupt condition.

DOI: https://doi.org/10.18500/1816-9791-2014-14-3-295-304

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UDC: 517.521

Citation: M. G. Magomed-Kasumov, “Approximation of Functions by Fourier–Haar Sums in Weighted Variable Lebesgue and Sobolev Spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:3 (2014), 295–304

Citation in format AMSBIB
\Bibitem{Mag14}
\by M.~G.~Magomed-Kasumov
\paper Approximation of Functions by Fourier--Haar Sums in Weighted Variable Lebesgue and Sobolev Spaces
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 3
\pages 295--304
\mathnet{http://mi.mathnet.ru/isu513}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-3-295-304}
\elib{https://elibrary.ru/item.asp?id=21967150}


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