Inverse Jackson theorems in spaces with integral metric

• Date: 2012
• Main Authors: Pichugov, S. A., Пичугов, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2581
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In the spaces $L_{\Psi}(T)$ of periodic functions with metric $\rho(f, 0)_{\Psi} = \int_T \Psi(|f(x)|)dx$, where $\Psi$ 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 the inver...