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30 p, 743.5 KB Two-Dimensional Hardy-Littlewood Theorem for Functions with General Monotone Fourier Coefficients / Oganesyan, Kristina (Centre de Recerca Matemàtica)
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.
2023 - 10.1007/s00041-023-10039-x
Journal of Fourier Analysis and Applications, Vol. 29, Issue 5 (October 2023) , art. 60  

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