Absolute convergence of double series of Fourier-Haar coefficients for functions of bounded p-variation

被引：7
作者：
B. I. Golubov
机构：
[1] Moscow Institute of Physical Technologies, State University, Dolgoprudnyi, Moscow Region, 141700
来源：
Russian Mathematics | 2012年 / 56卷 / 6期
基金：
俄罗斯基础研究基金会;
关键词：
Double Haar system; Fourier-Haar coefficients; Functions of two variables of bounded p-variation;
D O I：
10.3103/S1066369X12060011
中图分类号：
学科分类号：
摘要：
We consider functions of two variables of bounded p-variation of the Hardy type on the unit square. For these functions we obtain a sufficient condition for the absolute convergence of series of positive powers of Fourier coefficients with power-type weights with respect to the double Haar system. This condition implies those for the absolute convergence of series of Fourier-Haar coefficients of one-variable functions which have a bounded Wiener p-variation or belong to the class Lip a. We show that the obtained results are unimprovable. We also formulate N-dimensional analogs of the main result and its corollaries. © Allerton Press, Inc., 2012.
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页码：1 / 10
页数：9
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共 24 条
  • [11] Golubov B.I., On the fourier series of continuous functions with respect to a haar system, Izv Akad. Nauk SSSR. Ser. Matem., 28, 6, pp. 1271-1296, (1964)
  • [12] Bari N.K., Trigonometric Series, (1961)
  • [13] Hardy G.H., Weierstrass nondifferentiable function, Trans. Amer. Math. Soc., 17, pp. 301-325, (1916)
  • [14] Hardy G.H., On double fourier series and especially those which represent the double zeta-function with real and incommensurable parameters, Quart. J. Math., 37, 1, pp. 57-79, (1905)
  • [15] Ciesielski Z., On haar functions and on the shauder basis of the space c (0, 1), Bull. Acad. Polon. Sci., 7, pp. 227-232, (1959)
  • [16] Zygmund A., Trigonometric Series, (1959)
  • [17] Tabatadze G.Z., The absolute convergence of the fourier-haar series, Soobsch. Akad. Nauk GruzSSR, 103, 3, pp. 541-543, (1981)
  • [18] Tsagareishvili V.Sh., On the fourier-haar coefficients, Soobsch. Akad. Nauk GruzSSR, 81, 1, pp. 29-31, (1976)
  • [19] Goginava U., On the uniform summability of multiple walsh-fourier series, Anal. Math., 26, 3, pp. 209-226, (2000)
  • [20] Goginava U., Uniform convergence of N-dimensional trigonometric fourier series, Georgian Math. J., 7, 4, pp. 665-676, (2000)
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