Geodesic
Generalized Absolute Convergence of Single and Double Series in Multiplicative Systems
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 195-209.

Voir la notice de l'article provenant de la source Math-Net.Ru

Series of one- and two-dimensional Fourier coefficients in multiplicative systems $\chi$ (with bounded generating sequence ${\mathbf P}=\{p_i\}^\infty_{i=1}$) with weights satisfying Gogoladze–Meskhia-type conditions are studied. Sufficient conditions for the convergence of such series for continuous (in a generalized sense) functions and functions from ${\mathbf P}$-ary Hardy space are established. The question of whether these conditions are unimprovable is investigated. Sufficient conditions for generalized absolute convergence for functions of bounded $(\Lambda,\Psi)$-fluctuation are also established.
Keywords: multiplicative system, Gogoladze–Meskhia-type conditions, generalized absolute convergence, $\mathbf P$-ary Hardy space. 
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S. S. Volosivets; M. A. Kuznetsova. Generalized Absolute Convergence of Single and Double Series in Multiplicative Systems. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 195-209. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a2/

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