Geodesic
On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials
Sbornik. Mathematics, Tome 207 (2016) no. 12, pp. 1729-1742 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A nontrivial lower bound for the quantity $\sup_{t\in L}\|t\|_{\mathrm{QC}}/\|t\|_{\infty}$ is obtained for a subspace $L$ of $ \mathrm{T}(2^{m}-1)$ which satisfies a certain dimension condition. Bibliography: 8 titles.
Keywords: trigonometric polynomials, Rademacher functions.
Mots-clés : Fejér kernels 
@article{SM_2016_207_12_a5,
     author = {A. O. Radomskii},
     title = {On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials},
     journal = {Sbornik. Mathematics},
     pages = {1729--1742},
     year = {2016},
     volume = {207},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_12_a5/}
}
TY  - JOUR
AU  - A. O. Radomskii
TI  - On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials
JO  - Sbornik. Mathematics
PY  - 2016
SP  - 1729
EP  - 1742
VL  - 207
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2016_207_12_a5/
LA  - en
ID  - SM_2016_207_12_a5
ER  - 
%0 Journal Article
%A A. O. Radomskii
%T On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials
%J Sbornik. Mathematics
%D 2016
%P 1729-1742
%V 207
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2016_207_12_a5/
%G en
%F SM_2016_207_12_a5
A. O. Radomskii. On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials. Sbornik. Mathematics, Tome 207 (2016) no. 12, pp. 1729-1742. http://geodesic.mathdoc.fr/item/SM_2016_207_12_a5/

[1] B. S. Kashin, V. N. Temlyakov, “On a certain norm and related applications”, Math. Notes, 64:4 (1998), 551–554 | DOI | DOI | MR | Zbl

[2] B. S. Kashin, V. N. Temlyakov, “Ob odnoi norme i approksimatsionnykh kharakteristikakh klassov funktsii mnogikh peremennykh”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Sbornik statei, ed. S. M. Nikolskii, AFTs, M., 1999, 69–99 | MR

[3] B. S. Kashin, A. A. Saakyan, Orthogonal series, Transl. Math. Monogr., 75, Amer. Math. Soc., Providence, RI, 1989, xii+451 pp. | MR | MR | Zbl | Zbl

[4] P. G. Grigor'ev, “On a sequence of trigonometric polynomials”, Math. Notes, 61:6 (1997), 780–783 | DOI | DOI | MR | Zbl

[5] A. O. Radomskii, “On the possibility of strengthening Sidon-type inequalities”, Math. Notes, 94:5 (2013), 829–833 | DOI | DOI | MR | Zbl

[6] A. Zygmund, Trigonometric series, v. I, II, 2nd ed., Cambridge Univ. Press, New York, 1959, vii+354 pp. | MR | MR | Zbl | Zbl

[7] B. S. Kashin, “On certain properties of the space of trigonometric polynomials with uniform norm”, Proc. Steklov Inst. Math., 145 (1981), 121–127 | MR | Zbl

[8] R. A. Hunt, “On the convergence of Fourier series”, Orthogonal expansions and their continuous analogues (Edwardsville, Ill., 1967), Southern Illinois Univ. Press, Carbondale, Ill., 1968, 235–255 | MR | Zbl