Generalized Absolute Convergence of Series of Fourier Coefficients With Respect to Haar Type Systems

Abstract

For the orthogonal systems ofHaar type, introduced by Vilenkin in 1958, we study absolute convergence of series composed from positive powers of Fourier coefficients with multiplicators from the Gogoladze–Meskhia class. The conditions for convergence of the series are given in terms of either best approximations of functions in L p spaces by polynomials with respect to Haar type systems or fractional modulus of continuity for functions from the Wiener spaces V p , p > 1. We establish the sharpness of the obtained results.