Cite this article as:

Magomed-Kasumov M. G. Approximation of Functions by Fourier–Haar Sums in Weighted Variable Lebesgue and Sobolev Spaces . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 3, pp. 295-304. DOI: https://doi.org/10.18500/1816-9791-2014-14-3-295-304

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.521

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

Authors: 
Magomed-Kasumov Magomedrasul Grozbekovich, Daghestan Scientific Centre of the Russian Academy of Sciences, Makhachkala, Russia, Russia, 367025, Makhachkala, M. Gadjieva st., 45 , rasuldev@gmail.com, m_rasul@rambler.ru
Abstract: 

It is considered weighted variable Lebesgue Lp(x)w and Sobolev Wp(⋅),w spaces with conditions on exponent p(x)≥1 and weight w(x) that provide Haar system to be a basis in Lp(x)w. In such spaces there were obtained estimates of Fourier–Haar sums convergence speed. Estimates are given in terms of modulus of continuity Ω(f,δ)p(⋅),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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