Concerning a sufficient condition of sidon for the integrability of trigonometric series

We consider problems concerning integrability and convergence in the metric L of trigonometric series, the coefficientsa_k of which satisfy the conditions:a_k 0, there exist numbers A_k such that A_k 0, < , and ¦¦ A_k. The integrability of a series in cosines under these conditions is equivalent to a theorem of Sidon.Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 317–328, September, 1973.