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Approximation of functions by Fourier-Haar sums in weighted variable Lebesgue and Sobolev spaces. (Russian. English summary) Zbl 1301.42008
Summary: It is considered weighted variable Lebesgue $$L^{p(x)}_w$$ and Sobolev $$W_{p(\cdot), w}$$ spaces with conditions on exponent $$p(x)\geq 1$$ 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).
##### MSC:
 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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