Geodesic
Multipliers of Absolute Convergence
Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 433-443

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The paper deals with sequences of positive numbers $(d_n)$ such that, multiplying the Fourier coefficients $(C_n(f))$ of functions from given function classes by these numbers, one obtains a convergent series of the form $\sum|C_n(f)|^pd_n$, ${1\le p2}$. It is established that the resulting conditions cannot be strengthened in a certain sense. The results of the paper imply, in particular, some well-known results for trigonometric Fourier series.
Mots-clés : convergence, Fourier coefficients
Keywords: sequence of numbers. 
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     author = {V. Sh. Tsagareishvili and G. Tutberidze},
     title = {Multipliers of {Absolute} {Convergence}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {433--443},
     publisher = {mathdoc},
     volume = {105},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a10/}
}
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V. Sh. Tsagareishvili; G. Tutberidze. Multipliers of Absolute Convergence. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 433-443. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a10/