Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation

S. S. Volosivets ; A. N. Mingachev

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 78-90

Résumé

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.

Détail

Keywords: absolute convergence, multiplicative system, double series, generalized bounded fluctuation.

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