关于齐格蒙德和德布鲁因的不等式

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-09-15 DOI:10.1007/s10476-024-00048-3

R. R. Akopyan, P. Kumar, G. V. Milovanović

引用次数: 0

摘要

对于n度多项式\(P(z)\)的极坐标导数\(D_\alpha P(z) =nP(z)+(\alpha-z)P'(z)\) ，文献中的\(L^p\)不等式大多是针对\(\alpha\)的限制值的，而在本文中，我们将少数这样的基本结果扩展到复平面上的\(\alpha\)的所有值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the inequalities of Zygmund and de Bruijn

For the polar derivative \(D_\alpha P(z) =nP(z)+(\alpha-z)P'(z)\) of a polynomial \(P(z)\) of degree n, most of the \(L^p\) inequalities available in the literature are for restricted values of \(\alpha\), and in this paper we extend few such fundamental results to all of \(\alpha\) in the complex plane.

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.