Under some assumptions on the matrix of a summability method, whose rows are sequences of bounded variation, we obtain a generalization and an improvement of some results of Xie-Hua Sun and L. Leindler.
In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients satisfy certain conditions) the following order equality is proved where , , .
We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.