Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 489-498
Citer cet article
V. I. Ivanov. Certain inequalities in various metrics for trigonometric polynomials and their derivatives. Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 489-498. http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a1/
@article{MZM_1975_18_4_a1,
author = {V. I. Ivanov},
title = {Certain inequalities in various metrics for trigonometric polynomials and their derivatives},
journal = {Matemati\v{c}eskie zametki},
pages = {489--498},
year = {1975},
volume = {18},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a1/}
}
TY - JOUR
AU - V. I. Ivanov
TI - Certain inequalities in various metrics for trigonometric polynomials and their derivatives
JO - Matematičeskie zametki
PY - 1975
SP - 489
EP - 498
VL - 18
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a1/
LA - ru
ID - MZM_1975_18_4_a1
ER -
%0 Journal Article
%A V. I. Ivanov
%T Certain inequalities in various metrics for trigonometric polynomials and their derivatives
%J Matematičeskie zametki
%D 1975
%P 489-498
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a1/
%G ru
%F MZM_1975_18_4_a1
We establish for $0 the analog of the Bernstein–Zygmund inequality for the derivative of a trigonometric polynomial $$ \int_{-\pi}^\pi|t_n'(x)|^pdx\leqslant c_pn^p\int_{-\pi}^\pi|t_n(x)|^pdx. $$ We prove weighted inequalities, exact in the sense of order, for trigonometric polynomials and their derivatives in various integral metrics with exponents $0, $q\leqslant\infty$.
