On the Jackson theorem for periodic functions in metric spaces with integral metric. II

• Datum: 2011
• Hauptverfasser: Pichugov, S. A., Пичугов, С. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2011
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/2822
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

In the spaces $L_{\psi}(T^m)$ of periodic functions with metric $\rho(f, 0)_{\psi} = \int_{T^m}\psi(|f(x)|)dx$ , where $\psi$ is a function of the type of modulus of continuity, we study the direct Jackson theorem in the case of approximation by trigonometric polynomials. It is proved that the dir...