$L_{p}$不等式对于有限制零的多项式的增长

IF 0.5 Q3 MATHEMATICS

Archivum Mathematicum Pub Date : 2022-01-01 DOI:10.5817/am2022-3-159

N. A. Rather, Suhail Gulzar, A. Bhat

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引用次数: 0

摘要

。设P (z) = P n ν =0 a ν z ν是一个不消失于圆盘| z | < 1的最多n次的多项式，那么对于1≤P <∞和R > 1, Boas和Rahman证明了在0≤P <∞时，我们通过引入多项式P (z)的一些系数来改进上述不等式。给出了一类多项式P (z)在| z | > 1范围内无零的类似结果。

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$L_{p}$ inequalities for the growth of polynomials with restricted zeros

. Let P ( z ) = P n ν =0 a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1, then for 1 ≤ p < ∞ and R > 1, Boas and Rahman proved In this paper, we improve the above inequality for 0 ≤ p < ∞ by involving some of the coefficients of the polynomial P ( z ). Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.

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来源期刊

Archivum Mathematicum MATHEMATICS-

CiteScore

0.70

自引率

16.70%

发文量

审稿时长

35 weeks

期刊介绍： Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.