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

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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. 
@article{MZM_2020_107_2_a2,
     author = {S. S. Volosivets and M. A. Kuznetsova},
     title = {Generalized {Absolute} {Convergence} of {Single} and {Double} {Series} in {Multiplicative} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {195--209},
     publisher = {mathdoc},
     volume = {107},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a2/}
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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/