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 $\sum|C_n(f)|^pd_n$, ${1\le p<2}$. 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.
Keywords:convergence, Fourier coefficients, sequence of numbers.
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