Bernstein-Nikol'skii-type inequalities for trigonometric polynomials

Abstract

We obtain order estimates for Bernstein-Nikol’skii-type inequalities for trigonometric polynomials with an arbitrary choice of harmonics. It is established that in the case $ q = \infty $, $ 1 <p \leq2 $ these inequalities for trigonometric polynomials with arbitrary choice of harmonics and for ordinary trigonometric polynomials has different order of estimates.