Nikol’skii–Stechkin-Type Inequalities for the Increments of Trigonometric Polynomials in Metric Spaces

Abstract

In the spaces LΨ [0, 2𝜋] with the metric $$ \rho \left(f,0\right)\varPsi =\frac{1}{2\pi }{\int}_0^{2\uppi}\varPsi \left(|f(x)|\right) dx $$ , where is a function of Ψ the modulus-of-continuity type, we investigate an analog of the Nikol’skii–Stechkin inequalities for the increments and derivatives of trigonometric polynomials.