Inequalities for trigonometric polynomials in spaces with integral metric

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.