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

Let f and g be functions from different Lorentz spaces Lp, q[0, 1), h be theirmultiplicative convolution and xxxx be Fourier coefficients of h with respect to a multiplicative system with bounded generating sequence. We estimate the remainder of the series of xxxx with multiplicators of type kb in terms of the best approximations of f and g in the corresponding Lorentz spaces. We establish sharpness of this result and of its corollaries for the Lebesgue spaces. © 2017, Allerton Press, Inc.