Monotone extremal functions and the weighted Hilbert’s inequality

IF 0.5 4区数学 Q3 MATHEMATICS Portugaliae Mathematica Pub Date : 2023-02-28 DOI:10.4171/pm/2109

E. Carneiro, Friedrich Littmann

引用次数: 0

Abstract

In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert-Montgomery-Vaughan inequality.

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单调极值函数与加权希尔伯特不等式

在某些单调性条件下，我们找到了sgn函数的指数型最优单侧量。作为应用，我们利用这些特殊函数得到了(非尖锐)加权Hilbert-Montgomery-Vaughan不等式的简单傅里叶分析证明。

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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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.

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