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 = _T ψ (| f (x) |) dx , where ψ 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.