On the integration of one class ofN-dimensional trigonometric series

The Wiener algebra of absolutely convergent Fourier integrals: an overview

“…However, J. Marcinkiewicz proved the almost everywhere convergence of these "strong means" for each f ∈ L 1 (T) (see [175,Vol.2,Ch.XIII,§8] or [4, Ch.VII, §8]). There are essential generalizations of strong summability on T n in [45] and [78]. Let {ν m } ∞ m=0 be a strictly increasing sequence of natural numbers.…”

On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series

“…At present, some other conditions for the integrability of multiple trigonometric series of the form (1) are known [9]. However, the conditions obtained in the present paper are more convenient for application in a number of cases.…”