This is a preview of subscription content, log in via an institution to check access.
Literature cited
A. Zygmund, Trigonometric Series, Vol. II, Cambridge Univ. Press (1959).
V. L. Shapiro, “Circular summability C of double trigonometric series,” Trans. Am. Math. Soc.,76, No. 2, 223–233 (1954).
E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).
S. Bochner, “Theta relations with spherical harmonics,” Proc. Nat. Acad. Sci. USA,37, No. 12, 804–808 (1951).
E. M. Wright, “The asymptotic expansion of the generalized hypergeometric function,” J. London Math. Soc.,10, No. 4, 286–293 (1935).
N. S. Landkof, “Some remarks on stable random processes and α-superharmonic functions,” Mat. Zametki,14, No. 6, 901–912 (1973).
M. V. Fedoryuk, “Asymptotic behavior of Green's function of a parabolic pseudodifferential equation,” Differents. Uravn.,14, No. 7, 1296–1299 (1978).
B. I. Golubov, “Convergence of Gauss-Weierstrass type singular integrals for functions of several variables,” Dokl. Akad. Nauk SSSR,248, No. 5, 1044–1048 (1979).
V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1976).
P. P. Korovkin, “On an asymptotic property of positive methods of summation of Fourier series and on the best approximation of functions of the class Z2 by positive linear operators,” Usp. Mat. Nauk,13, No. 6, 99–103 (1958).
V. A. Yudin, “The multidimensional Jackson theorem,” Mat. Zametki,20, No. 3, 439–444 (1976).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 30, No. 5, pp. 749–762, November, 1981.
Rights and permissions
About this article
Cite this article
Golubov, B.I. Asymptotic behavior of singular multiple integrals for differentiable functions. Mathematical Notes of the Academy of Sciences of the USSR 30, 873–880 (1981). https://doi.org/10.1007/BF01140223
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01140223