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We prove the Hardy-Littlewood theorem in two dimensions for functions whoseFourier coefficients obey general monotonicity conditions and, importantly, arenot necessarily positive. The sharpness of the result is given by acounterexample, which shows that if one slightly extends the considered classof coefficients, the Hardy-Littlewood relation fails.

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