Multipliers of Absolute Convergence

Abstract

The paper deals with sequences of positive numbers (d_n) such that, multiplying the Fourier coefficients (C_n(f)) of functions from given function classes by these numbers, one obtains a convergent series of the form \(\sum {{\rm{|}}{C_n}(f){{\rm{|}}^p}{d_n}, 1 \le p < 2} \). 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.