Generalization of the Hardy-Littlewood theorem on Fourier series
Фурье қатары туралы Харди-Литтлвуд теоремасының жалпыламасы
Обобщение теоремы Харди-Литтлвуда о рядах Фурье
Bitimkhan S.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#104Issue 449 - 55 pp.
In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance. Multidimensional versions of this theorem have been extensively studied for the Lebesgue space. Significant differences of the multidimensional variants in comparison with the one-dimensional case are revealed and the strengthening of this theorem is obtained. The Hardy-Littlewood theorem is also generalized for various function spaces and various types of monotonicity of the series coefficients. Some of these generalizations can be seen in works of M.F. Timan, M.I. Dyachenko, E.D. Nursultanov, S. Tikhonov. In this paper, a generalization of the Hardy-Littlewood theorem for double Fourier series of a function in the space Lqϕ(Lq)(0,2π]2 is obtained.
Fourier coefficients , Fourier series , Hardy-Littlewood theorem , Lebesgue space , trigonometric series
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Karagandy University of the Name of Academician E.A. Buketov, Kazakhstan
Karagandy University of the Name of Academician E.A. Buketov
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