On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series - Ivashchuk, O. V.; Zaderei, P. V.; Pelagenko, E. N. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
For the trigonometric series _k=0^∞a_k_lkV (k-1)Ve^i(l, x), a_k→ 0,k→ ∞, given on [-π, π)^m, where V is some polyhedron in R^m, we prove that the inequality _T^m|^∞_k=0 a_k _lkV(k-1)Ve^i(l, x) | dx ≤ C ^∞_k=0 (k+1) |Δ A_k|, holds if the coefficients a_k satisfy the following conditions of the Sidon - Telyakovskii type: A_k→∞,|Δ a_k| ≤ A_k, k ≥ 0, ^∞_k=0(k+1) |Δ A_k|