Best approximation of functions by polynomials with respect to multiplicative systems and generalized monotonicity

摘要

We present two Konyuskov type theorems on the equivalence of O- and -relations between the generalized Fourier-Vilenkin coefficients and the best approximations in L (p) and p-fluctuation metrics. We also obtain estimates of the best approximation of a function by transformed Fourier-Vilenkin series in these metrics.