Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Magomed-Kasumov M. M. Approximation of Functions by Fourier–Haar Sums in Weighted Variable Lebesgue and Sobolev Spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 295-304. DOI: 10.18500/1816-9791-2014-14-3-295-304, EDN: SMSJVV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.09.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.521
DOI: 
10.18500/1816-9791-2014-14-3-295-304
EDN: 
SMSJVV

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

Autors: 
Magomed-Kasumov Magomedrasul Magomedrasul, Daghestan Scientific Centre of Russian Academy of Sciences
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
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Received: 
18.03.2014
Accepted: 
18.07.2014
Published: 
10.09.2014
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