Integral inequalities for algebraic and trigonometric polynomials / Arestov V. V.,Glazyrina P. Yu. // DOKLADY MATHEMATICS. - 2012. - V. 85, l. 1. - P. 104-108.

ISSN/EISSN:

1064-5624 / нет данных

Type:

Article

Abstract:

In this paper, we consider sharp estimates of integral functionals for functions phi defined on the semiaxis (0, a) and operators L on the set T (n) of real trigonometric polynomials f (n) of order n a parts per thousand yen 1 by the uniform norm of the polynomials. We also consider similar problems for algebraic polynomials on the unit circle of the complex plane. P. Erdos, A. Calderon, G. Klein, L. V. Taikov, and others investigated such inequalities. In particular, we show that, for 0 a parts per thousand currency sign q < a, the sharp inequality holds on the set T (n) , n a parts per thousand yen 1, for the Weyl fractional derivatives D (alpha) f (n) of order alpha a parts per thousand yen 1. For q = a (alpha a parts per thousand yen 1), this fact was proved by P.I. Lizorkin (1965). For 1 a parts per thousand currency sign q < a and positive integer alpha, the inequality was proved by L.V. Taikov (1965); however, in this case, the inequality follows from results of an earlier paper by A. P. Calderon and G. Klein (1951).

Author keywords:

нет данных

DOI:

10.1134/S1064562412010371

Web of Science ID:

ISI:000301798700027

Соавторы в МНС:

Другие поля

Поле	Значение
Month	FEB
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	Vitalii.Arestov@usu.ru Polina.Glazyrina@usu.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}11-01-00462]; Ural Branch of the Russian Academy of Sciences {[}09-S-1-1007]; Siberian Branch of the Russian Academy of Sciences {[}09-S-1-1007]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project no. 11-01-00462); the work of the second author was also supported by the Integration Project for Fundamental Research of the Ural and Siberian Branches of the Russian Academy of Sciences (project no. 09-S-1-1007).
Number-of-Cited-References	15
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	20
Journal-ISO	Dokl. Math.
Doc-Delivery-Number	912LE