This is a preview of subscription content, log in via an institution to check access.
Literature Cited
I. L. Bloshanskii, “On the equiconvergence of expansions in a multiple trigonometric Fourier series and Fourier integral,” Mat. Zametki,18, No. 2, 153–168 (1975).
A. Zygmund, Trigonometric Series. Vol. II, Cambridge Univ. Press, Cambridge (1959).
I. L. Bloshanskii, “On the equiconvergence of the multiple Fourier series and Fourier integral expansions in the case of square summation,” Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 3, 685–705 (1976).
N. R. Tevzadze, “On the convergence of the double Fourier series of a square summable function,” Soobshch. Akad. Nauk GruzinSSR,58, No. 2, 277–279 (1970).
P. Sjolin, “Convergence almost everywhere of certain singular integrals and multiple Fourier series,” Ark. Mat.,9, No. 1, 65–90 (1971).
A. Kolmogoroff, “Une serie de Fourier-Lebesgue divergente presque partout,” Fund. Math.,4, 324–328 (1923).
N. K. Bary, A Treatise on Trigonometric Series, I and II, Macmillan, New York (1964).
E. M. Stein, “On limits of sequences of operators,” Ann. Math.,74, No. 1, 140–170 (1961).
J.-P. Kahane, Some Random Series of Functions, Heath, Lexington, Mass. (1968).
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Univ. Press, London (1938).
Additional information
Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 39–52, January–February, 1990.
Rights and permissions
About this article
Cite this article
Bloshanskii, I.L. Multiple fourier integral and multiple fourier series under square summation. Sib Math J 31, 30–42 (1990). https://doi.org/10.1007/BF00971147
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971147