Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-19 DOI:10.1007/s00041-023-10039-x

Kristina Oganesyan

引用次数: 0

Abstract

Abstract We prove the Hardy–Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample, which shows that if one slightly extends the considered class of coefficients, the Hardy–Littlewood relation fails.

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一般单调傅里叶系数函数的二维Hardy-Littlewood定理

摘要在二维条件下证明了傅里叶系数服从一般单调性条件的函数的Hardy-Littlewood定理，重要的是，它不一定是正的。通过一个反例给出了结果的清晰性，该反例表明，如果稍微扩展所考虑的系数类别，Hardy-Littlewood关系将失效。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.