Literature Cited
N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz (1961).
N. Wiener, “The quadratic variation of a function and its Fourier coefficients,” Massachusetts J. Math.,3, 72–94 (1924).
J. Marcinkiewicz, “On a class of functions and their Fourier series,” Compt. Rend. Soc. Sci.,26, 71–77, Varsovie (1934).
L. C. Young, “General inequalities for Stieltjes integrals and the convergence of Fourier series,” Math. Ann.,115, 581–612 (1938).
R. Salem, “Essais sur les series trigonometriques,” Actualite Sci. et Industr., No. 862, Paris (1940).
A. Baernstein, “On the Fourier series of functions of bounded Ф-variation,” Studia Math.,42, No. 3, 243–248 (1972).
K. I. Oskolkov, “Generalized variation, Banach's indicatrix and uniform convergence of Fourier series,” Matem. Zam.,12, No. 3, 313–324 (1972).
C. H. Hardy, “On double Fourier series and especially those which represent the double zeta-function with real and incommensurable parameters,” Quart. J. Math.,37, No. 1, 53–79 (1906).
B. I. Golubov, “Functions of generalized bounded variation, convergence of their Fourier series and adjoint trigonometric series,” Dokl. AN SSSR,205, No. 6, 1277–1280 (1972).
B. I. Golubov, “Convergence of Riesz spherical means of multiple Fourier series and integrals for functions of bounded generalized variation,” Matem. Sb.,89, No. 4, 630–653 (1972).
M. A. Krasnosel'skii and Ya. B. Rutitskii, Convex Spaces and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).
L. V. Zhizhiashvili, Conjugate Functions and Trigonometric Series [in Russian], Izd-vo TGU, Tbilisi (1969).
F. Ustina, “Convergence of double Fourier series,” Ann. Mat. Pura ed Appl., No. 85, 21–47 (1970).
I. E. Zhak, “Conjugate double trigonometric series,” Matem. Sb.,31, No. 3, 469–484 (1952).
A. A. Bukhshtab, Trigonometric Series [in Russian], Vol. 1, Mir, Moscow (1965).
L. V. Zhizhiashvili, Conjugate Functions and Trigonometric Series, Ph. D. Thesis [in Russian], MGU (1967).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 2, pp. 262–291, March–April, 1974.
Rights and permissions
About this article
Cite this article
Golubov, B.I. Convergence of double Fourier series for functions of bounded generalized variation. Pt. 1. Sib Math J 15, 183–204 (1974). https://doi.org/10.1007/BF00968284
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968284