2017
Том 69
№ 9

# Inequalities for trigonometric polynomials in spaces with integral metric

Pichugov S. A.

Abstract

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 analogs of the classic Bernstein inequalities for the norms of derivatives and increments of trigonometric polynomials.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 12, pp 1883-1899.

Citation Example: Pichugov S. A. Inequalities for trigonometric polynomials in spaces with integral metric // Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1657-1671.

Full text