A note on the Kolmogorov-type inequalities for more than three norms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911479313203200 |
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| author | Kovalenko, Oleg |
| author_facet | Kovalenko, Oleg |
| contents | In this note we show that sharp Kolmogorov-type inequalities that estimate the uniform norm $\|f^{(k)}\|$ of the $k$-th derivative of a function $f\colon \mathbb{R}\to\mathbb{R}$ by the values of the uniform norm of $f$ and uniform norms of several its higher derivatives ($\|f^{(r)}\|$ and $\|f^{(r-1)}\|$, or $\|f^{(r)}\|$ and $\|f^{(r-2)}\|$, or $\|f^{(r)}\|$, $\|f^{(r-1)}\|$ and $\|f^{(r-2)}\|$) using standard techniques can be obtained from the known solutions to the Kolmogorov problem about existence of a function with given norms of its derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the Kolmogorov-type inequalities for more than three norms Kovalenko, Oleg Functional Analysis 26D10, 41A44, 41A17 In this note we show that sharp Kolmogorov-type inequalities that estimate the uniform norm $\|f^{(k)}\|$ of the $k$-th derivative of a function $f\colon \mathbb{R}\to\mathbb{R}$ by the values of the uniform norm of $f$ and uniform norms of several its higher derivatives ($\|f^{(r)}\|$ and $\|f^{(r-1)}\|$, or $\|f^{(r)}\|$ and $\|f^{(r-2)}\|$, or $\|f^{(r)}\|$, $\|f^{(r-1)}\|$ and $\|f^{(r-2)}\|$) using standard techniques can be obtained from the known solutions to the Kolmogorov problem about existence of a function with given norms of its derivatives. |
| title | A note on the Kolmogorov-type inequalities for more than three norms |
| topic | Functional Analysis 26D10, 41A44, 41A17 |
| url | https://arxiv.org/abs/2603.02044 |