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