Abstract
We prove that, for every 0 < ϵ < 1, there exists a measurable set E ⊂ T = [0, 1]2 with measure ∣E∣ > 1 − ϵ such that, for all f ∈ L1(T) and 0 < η < 1, we can find \(\tilde f \in {L^1}(T)\) with \(\int\!\!\!\int_T {{\rm{|}}f(x,y) - \tilde f(x,y){\rm{|}}dxdy \le \eta } \) coinciding with f(x, y) on E whose double Fourier-Franklin series converges absolutely to f almost everywhere on T.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 513–527.
The authors were supported by the Science Committee of Ministry of Education and Science of the Republic of Armenia (Grants 18-1A074 and 18-1A148).
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Gevorkyan, G.G., Grigoryan, M.G. Absolute Convergence of the Double Fourier-Franklin Series. Sib Math J 61, 403–416 (2020). https://doi.org/10.1134/S0037446620030039
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DOI: https://doi.org/10.1134/S0037446620030039