Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912384421986304 |
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| author | Ganzburg, Michael I Saucedo, Miquel Tikhonov, Sergey |
| author_facet | Ganzburg, Michael I Saucedo, Miquel Tikhonov, Sergey |
| contents | 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 $s$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter Ganzburg, Michael I Saucedo, Miquel Tikhonov, Sergey Classical Analysis and ODEs 41A17 (Primary), 42A05 Secondary) 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 $s$. |
| title | Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter |
| topic | Classical Analysis and ODEs 41A17 (Primary), 42A05 Secondary) |
| url | https://arxiv.org/abs/2403.13149 |