The Bernstein-Szego Inequality for Fractional Derivatives of Trigonometric Polynomials / Arestov V. V.,Glazyrina P. Yu. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 288, l. 1. - P. S13-S28.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

On the set A, of trigonometric polynomials of degree n >= 1 with complex coefficients, we consider the Szego operator D-theta(alpha) defined by the relation D-theta(alpha) f(n) (t) = cos theta D-alpha f(n) (t) sin theta D-alpha f(n) (t) for alpha, theta is an element of R N, where alpha >= 0. Here, D-alpha f(n) P f and D(alpha)f(n) are the Weyl fractional derivatives of (real) order a of the polynomial f of its conjugate /Th. In particular, we that, if a > n In 2n, then, for any 0 E N, the sharp inequality Mcos 0 D' f sin 0 D prove p f L, holds on the set 3;-Th in the spaces Lp for all p >= 0. For classical derivatives (of integer order a > 1), this inequality was obtained by Szego in the uniform norm (p = infinity) in 1928 and by Zygmund for 1 <= p <= infinity in 1931-1935. For fractional derivatives of (real) order alpha >= 1 and 1 <= p <= infinity, the inequality was proved by Kozko in 1998.

Author keywords:

trigonometric polynomial; Weyl fractional derivative; Bernstein inequality; Szego inequality INTEGRAL-INEQUALITIES

DOI:

10.1134/S0081543815020030

Web of Science ID:

ISI:000352991400002

Соавторы в МНС:

Другие поля

Поле	Значение
Month	APR
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	INTEGRAL-INEQUALITIES
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	Vitalii.Arestov@urfu.ru Polina.Glazyrina@urfu.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}11-01-00462, 12-01-31495]; Ministry of Education and Science of the Russian Federation {[}1.5444.2011]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00462 and 12-01-31495), by the Ministry of Education and Science of the Russian Federation (state contract no. 1.5444.2011), and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References	31
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	8
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	CG0VY