Geodesic
On one inequality of different metrics for trigonometric polynomials
Ural mathematical journal, Tome 8 (2022) no. 2, pp. 27-45

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We study the sharp inequality between the uniform norm and $L^p(0,\pi/2)$-norm of polynomials in the system $\mathscr{C}=\{\cos (2k+1)x\}_{k=0}^\infty$ of cosines with odd harmonics. We investigate the limit behavior of the best constant in this inequality with respect to the order $n$ of polynomials as $n\to\infty$ and provide a characterization of the extremal polynomial in the inequality for a fixed order of polynomials.
Keywords: trigonometric cosine polynomial in odd harmonics, Nikol'skii different metrics inequality. 
@article{UMJ_2022_8_2_a2,
     author = {Vitalii V. Arestov and Marina V. Deikalova},
     title = {On one inequality of different metrics for trigonometric polynomials},
     journal = {Ural mathematical journal},
     pages = {27--45},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a2/}
}
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Vitalii V. Arestov; Marina V. Deikalova. On one inequality of different metrics for trigonometric polynomials. Ural mathematical journal, Tome 8 (2022) no. 2, pp. 27-45. http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a2/