Partial best approximations and magnitude of
double Fourier–Vilenkin coefficients

Abstract. We give estimates for the magnitude of double Vilenkin–Fourier coefficients of functions from generalized Hölder spaces, some \(p\)-fluctuational spaces and bounded
\(\Lambda\)–\(\Gamma\)–\(\varphi\)-fluctuation spaces. For Hölder and \(p\)-fluctuational spaces we establish the sharpness of these estimates. Also we establish relation between full and partial best approximations and Watari–Efimov type inequality concerning partial best approximation and partial modulus of continuity.