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

Abstract

Let f and g be functions from different Lorentz spaces L p, 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 k b 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.