Abstract
The uniform convergence of the partial sums, relative to a system of homothetic starlike polygons, is considered. Among other things, it is established an arbitrary preassigned positive sequence from ℓλℤλ can be majorized by the coefficients of a uniformly convergent double Fourier series.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
S. V. Kislyakov, “Fourier coefficients of boundary values of functions that are analytic in the disc and in the bidisc,” Trudy Mat. Inst. Akad. Nauk SSSR,155, 77–94 (1981).
S. V. Kislyakov, “The quantitative aspect of correction theorems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,92, 182–191 (1979).
S. V. Kislyakov, “Fourier coefficients of continuous functions and a class of multipliers,” Ann. Inst. Fourier,38, No. 2, 147–183 (1988).
S. V. Kislyakov (S. V. Kisliakov), “A substitute for the weak type (1, 1) inequality for multiple Riesz projections,” in: Linear and Complex Analysis Problem Book, Lecture Notes in Math., No. 1043, Springer, Berlin (1984), 322–324.
S. A. Vinogradov, “A refinement of Kolmogorov's theorem on the conjugate function and interpolational properties of uniformly convergent power series,” Trudy Mat. Inst. Akad. Nauk SSSR,155, 7–40 (1981).
J. Bourgain, “Bilinear forms on H∞ and bounded bianalytic functions,” Trans. Amer. Math. Soc.,286, No. 1, 313–337 (1986).
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton (1970).
S. V. Kislyakov and N. G. Sidorenko, “Absence of a local unconditional structure in anisotropic spaces of smooth functions,” Sib. Mat. Zh.,29, No. 3, 64–77 (1988).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 151–162, 1989.
Rights and permissions
About this article
Cite this article
Kislyakov, S.V. On uniformly convergent double Fourier series. J Math Sci 61, 2038–2044 (1992). https://doi.org/10.1007/BF01095667
Issue Date:
DOI: https://doi.org/10.1007/BF01095667