Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter
Abstract
In this paper, we study the form of the constant C in the Bernstein--Nikolskii inequalities \|f(s)\|q C(s, p, q)\|f\|p,\,0<p<q ≤∞, for trigonometric polynomials and entire functions of exponential type. We obtain the optimal behavior of the constant with respect to the smoothness parameter s.
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