Abstract:
In this paper, we studied the issues of integrability with the weight of the sum of series with respect
to multiplicative systems, provided that the coefficients of the series are monotonic. The conditions for
the weight function and the series’ coefficients are found; the sum of the series belongs to the weighted
Lebesgue space Lp (1 < p < ∞). In addition, the case of p = 1 was considered. In this case, other
conditions for the weighted integrability of the sum of the series under consideration are found. In the
case of the generating sequence’s boundedness, the proved theorems imply an analogue of the well-known
Hardy-Littlewood theorem on trigonometric series with monotone coefficients.
