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arXiv · 2208.14405

Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients

Kristina Oganesyan
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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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Kristina Oganesyan. 2022-08-30. Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients. https://doi.org/10.1007/s00041-023-10039-x

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