Inverse Jackson theorems in spaces with integral metric

摘要

In the spaces L_ψ(T) of periodic functions with metric ρ(f, 0)_ψ= ∫_T ψ ({pipe}f(x){pipe})dx, where ψ is a function of the modulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that an inverse Jackson theorem is true if and only if the lower dilation exponent of the function ψ is not equal to zero.