Inverse Jackson theorems in spaces with integral metric - Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
In the spaces $L_{Ψ}(T)$ of periodic functions with metric $ρ(f, 0)_{Ψ} = \int_T Ψ(|f(x)|)dx$, where $Ψ$ is a function of themodulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that the inverse Jackson theorem is true if and only if the lower dilation exponent of the function $Ψ$ is not equal to zero.