Geodesic
Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 78-90

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The series of one-dimensional and two-dimensional Fourier coefficients with respect to multiplicative systems $\chi$ (with a 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 are established for functions from different classes of generalized bounded fluctuation.
Keywords: absolute convergence, multiplicative system, double series, generalized bounded fluctuation. 
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     author = {S. S. Volosivets and A. N. Mingachev},
     title = {Generalized absolute convergence of {Fourier} series with respect to multiplicative systems of functions of generalized bounded fluctuation},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {78--90},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a7/}
}
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S. S. Volosivets; A. N. Mingachev. Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 78-90. http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a7/