Polynomial approximation with respect to multiplicative systems in the Morrey space

We establish the main theorems on polynomial approximation with respect to multiplicative systems in the Morrey space and estimate the best approximations and the moduli of smoothness of functions in terms of the growth of the generalized derivatives of their best approximation polynomials, Fourier sums, and Riesz–Zygmund means with respect to multiplicative systems. Also, we provide some criteria for a function to belong to the classes with prescribed majorants for the modulus of smoothness or best approximation in the Morrey space.