Abstract
It is proved that for anyf(x, y) ∈ L(R), where R=[-π,π,-π, π], a function ϕ(x, y), exists such that ¦ϕ(x, y) ¦=¦f(x, y) ¦ for almost all (x, y) ∈ R. The Fourier series of the function ϕ(x, y) and all conjugate trigonometric series are A*-summable almost everywhere.
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Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 145–150, February, 1972.
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Gogoladze, L.D. The question of A*-summability of double trigonometric Fourier series. Mathematical Notes of the Academy of Sciences of the USSR 11, 93–96 (1972). https://doi.org/10.1007/BF01097923
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DOI: https://doi.org/10.1007/BF01097923