Geodesic
$\alpha$-monotone sequences and the Lorentz theorem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2023), pp. 63-67

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Properties of $\alpha$-monotone sequences are studied. A relationship between $\alpha$-monotonicity and the limiting rate of change of coefficients is revealed. Operations on sequences that do not lead out of the class $M_\alpha$ are discussed. An analogue of the Lorentz theorem for trigonometric series with coefficients from the classes $M_\alpha$ for $0 \alpha 1$ is proved. 
@article{VMUMM_2023_2_a7,
     author = {E. D. Alferova and M. I. Dyachenko},
     title = {$\alpha$-monotone sequences and the {Lorentz} theorem},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {63--67},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a7/}
}
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E. D. Alferova; M. I. Dyachenko. $\alpha$-monotone sequences and the Lorentz theorem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2023), pp. 63-67. http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a7/