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arXiv · 2403.13149

Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter

Michael I Ganzburg·Miquel Saucedo·Sergey Tikhonov
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Abstract

In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $\|f^{(s)}\|_q \lesssim C(s, p, q)\left\|f\right\|_p,\,0<p<q \leq\infty$, 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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Michael I Ganzburg, Miquel Saucedo, Sergey Tikhonov. 2024-03-19. Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter. https://arxiv.org/abs/2403.13149

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