Literature cited
Yu. A. Ponomarenko, “Some criteria for the absolute Cesaro summability of Fourier multiple series,” Dokl. AN SSSR,152, No. 6 (1963).
M. F. Timan and Yu. A. Ponomarenko, “Some criteria for the absolute summability of Fourier series,” in: Investigations on Current Problems in the Constructive Theory of Functions [in Russian], Baku (1965).
M. F. Timan, “On the absolute convergence of Fourier multiple series,” Dokl. AN SSSR,137 (1961).
M. F. Timan, “The partial best approximations of functions, the absolute convergence of Fourier series and the nuclearity of Hilbert-Schmidt integral operators,” Mat. Sb.,75, No. 3 (1968).
S. B. Stechkin, “On the absolute convergence of orthogonal series,” Dokl. AN SSSR,102 (1955).
M. F. Timan, “On the absolute convergence and summability of Fourier series,” Soobshch. AN GruzSSR,26, No. 6 (1961).
M. F. Timan, “Remarks on the problem of the absolute summability of orthogonal series,” Dokl. AkrSSR, No. 12 (1966).
A. V. Grepachevskaya, “The absolute summability of orthogonal series,” Mat. Sb.,65(107), No. 3 (1964).
H. Leindler, “Uber die absolute summierkeit der orthogonalreihen,” Acta Sci. Math. Szeged,22, 243–268 (1961).
I. E. Zhak and M. F. Timan, “On the summation of double series,” Mat. Sb.,35(77), No. 1 (1953).
A. A. Konyushkov, “The best approximations by trigonometric polynomials,” Mat. Sb.,44(86), No. 11 (1958).
E. Kogbetlaintz, Bull. Sci. Math.,2, 49, 252 (1925).
I. E. Zhak, “The absolute summability of double numerical series,” Dokl. AN SSSR,73, No. 4 (1950).
G. H. Hardy, D. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge (1934).
M. F. Timan, “Some questions on the constructive theory of functions of several variables,” in: Investigations on Current Problems in the Constructive Theory of Functions [in Russian], Fizmatgiz, Moscow (1961).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 23, No. 3, pp. 346–361, May–June, 1971.
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Ponomarenko, Y.A., Timan, M.F. On the absolute summability of Fourier multiple series. Ukr Math J 23, 291–304 (1971). https://doi.org/10.1007/BF01085351
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DOI: https://doi.org/10.1007/BF01085351