Multipliers of Absolute Convergence.

The paper deals with sequences of positive numbers (dn) such that, multiplying the Fourier coefficients (Cn(f)) of functions from given function classes by these numbers, one obtains a convergent series of the form ∑ | C n (f) | p d n , 1 ≤ p < 2 . It is established that the resulting conditions cannot be strengthened in a certain sense. The results of the paper imply, in particular, some well-known results for trigonometric Fourier series. [ABSTRACT FROM AUTHOR]