2017
Том 69
№ 9

All Issues

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

Pichugov S. A.


Abstract

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 trigonometric polynomials.

Citation Example: Pichugov S. A. Nikol’skii – Stechkin-type inequalities for the increments of trigonometric polynomials in metric spaces // Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 711-716.