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 Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 5, Pages 32–44 (Mi ivm9235)

Multiplicative convolutions of functions from Lorentz spaces and convergence of series from Fourier–Vilenkin coefficients

S. S. Volosivets, M. A. Kuznetsova

Saratov State National Research University, 83 Astrakhanskya str., Saratov, 410012 Russia

Abstract: Let $f$ and $g$ be functions from different Lorentz spaces $L^{p,q}[0,1)$, $h$ be their multiplicative convolution and $\widehat{h}(k)$ be Fourier coefficients of $h$ with respect to a multiplicative system with bounded generating sequence. We estimate the remainder of the series of $|\widehat{h}(k)|^a$ with multiplicators of type $k^b$ in terms of best approximations of $f$ and $g$ in corresponding Lorentz spaces. We establish the sharpness of this result and its corollaries for Lebesgue spaces.

Keywords: Lorentz space, multiplicative system, Fourier coefficients, multiplicative convolution, best approximation.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.1520.2014/K

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:5, 26–37

Bibliographic databases:

UDC: 517.518

Citation: S. S. Volosivets, M. A. Kuznetsova, “Multiplicative convolutions of functions from Lorentz spaces and convergence of series from Fourier–Vilenkin coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 5, 32–44; Russian Math. (Iz. VUZ), 61:5 (2017), 26–37

Citation in format AMSBIB
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