Volosivets S. S.
Approximation by polynomials with respect to multiplicative systems in weighted Lp-spaces
We study best approximations of polynomials with respect to multiplicative systems in the Lp -spaces with Muckenhoupt weights. Using Jackson’s and Bernstein’s inequalities, we obtain the direct and inverse approximation theorems in terms of the K-functional and the inverse theorem of the Timan-Besov type. In the case of a power weight, we give a criterion for the membership of a function in the weighted Lp-space in terms of the Fourier coefficients with respect to multiplicative systems.