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

被引：0

作者：

Oganesyan, Kristina ^{[1
,2
]}

机构：

[1] Univ Autonoma Barcelona, Ctr Recerca Matemat, Barcelona, Spain

[2] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2023年 / 29卷 / 05期

关键词：

Fourier series; General monotone coefficients; Hardy-Littlewood theorem; TRIGONOMETRIC SERIES; INTEGRABILITY; CONVERGENCE; INEQUALITIES; SMOOTHNESS; MODULI; SINE;

D O I：

10.1007/s00041-023-10039-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：30

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