Abstract
We consider the sine series $$\mathop \sum \limits_{k = 1}^\infty a_k \sin kx$$ with monotone coefficients tending to zero and denote byg(x) its sum. We establish estimates of the integral ∝¦g¦dx over a given subinterval of (0,π]. These estimates are uniform with respect to the coefficientsak and the endpoints of the subinterval. In the particular case wheng is not integrable over the period, we get an asymptotic estimate of the growth order of the integral over [∈, π] as∈↓+0. It is of the same form as in the case of series with convex coefficients.
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