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 Mat. Zametki, 2019, Volume 105, Issue 3, Pages 433–443 (Mi mz12297)

Multipliers of Absolute Convergence

V. Sh. Tsagareishvili, G. Tutberidze

Tbilisi Ivane Javakhishvili State University

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.

 Funding Agency Grant Number Shota Rustaveli National Science Foundation PHDF-18-476 This work was supported by the Shota Rustaveli National Science Foundation of Georgia under grant PHDF-18-476.

DOI: https://doi.org/10.4213/mzm12297

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UDC: 517.521
Revised: 11.06.2018

Citation: V. Sh. Tsagareishvili, G. Tutberidze, “Multipliers of Absolute Convergence”, Mat. Zametki, 105:3 (2019), 433–443

Citation in format AMSBIB
\Bibitem{TsaTut19} \by V.~Sh.~Tsagareishvili, G.~Tutberidze \paper Multipliers of Absolute Convergence \jour Mat. Zametki \yr 2019 \vol 105 \issue 3 \pages 433--443 \mathnet{http://mi.mathnet.ru/mz12297} \crossref{https://doi.org/10.4213/mzm12297} \elib{http://elibrary.ru/item.asp?id=37045131}