Inequalities for trigonometric polynomials in spaces with integral metric - Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
In the spaces $L_{ψ}(T)$ of periodic functions with metric $ρ( f , 0)_{ψ} = \int_T ψ (| f (x) |) dx $, where $ψ$ is afunction of the modulus-of-continuity type, we investigate analogs of the classic Bernstein inequalities for thenorms of derivatives and increments of trigonometric polynomials.