Geodesic
Multiplicative convolutions of functions from Lorentz spaces and convergence of series from Fourier--Vilenkin coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 32-44

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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, best approximation.
Mots-clés : Fourier coefficients, multiplicative convolution 
@article{IVM_2017_5_a3,
     author = {S. S. Volosivets and M. A. Kuznetsova},
     title = {Multiplicative convolutions of functions from {Lorentz} spaces and convergence of series from {Fourier--Vilenkin} coefficients},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {32--44},
     publisher = {mathdoc},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_5_a3/}
}
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%A M. A. Kuznetsova
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%D 2017
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S. S. Volosivets; M. A. Kuznetsova. Multiplicative convolutions of functions from Lorentz spaces and convergence of series from Fourier--Vilenkin coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 32-44. http://geodesic.mathdoc.fr/item/IVM_2017_5_a3/