Nikol’skii – Stechkin-type inequalities for the increments of trigonometric polynomials in metric spaces

• Date: 2017
• Main Authors: Pichugov, S. A., Пичугов, С. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1730
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In the spaces $L_{\Psi} [0, 2\pi ]$ with the metric $$\rho (f, 0)\Psi = \frac1{2\pi }\int^{2\pi }_0 \Psi (| f(x)| ) dx,$$ where $\Psi$ is a function of the modulus-ofcontinuity type, we investigate an analog of the Nikol’skii – Stechkin inequalities for the increments and derivatives of trigonome...