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On the localization of rectangular partial sums for multiple Fourier series

Author: Fon Che Liu
Journal: Proc. Amer. Math. Soc. 34 (1972), 90-96
MSC: Primary 42A92; Secondary 42A62
MathSciNet review: 0294993
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Abstract: The question of the localization for rectangular partial sums of the multiple Fourier series for functions of Sobolev spaces is settled.

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  • [1] L. Cesari, Sulle funzioni di piu variabili generalmente a variazione limitatae sulla convergenza delle relative serie multiple di Fourier, Commentationes, Pontificia Academia Scientiarum, Vol. III, N.7, 171-197.
  • [2] C. Goffman and F. C. Liu, On the localization property of square partial sums for multiple Fourier series, Studia Math. (to appear). MR 0312147 (47:709)
  • [3] V. A. Il'in, Problems of localization and convergence for Fourier series in fundamental systems of functions of the Laplace operator, Uspehi Mat. Nauk 23 (1968), no. 2 (140), 61-120=Russian Math. Surveys 23 (1968), no. 2, 59-116. MR 36 #6870. MR 0223823 (36:6870)
  • [4] B. M. Levitan, On summability of multiple series and Fourier integrals, Dokl. Akad. Nauk SSSR 102 (1955), 1073-1076. (Russian) MR 17, 32. MR 0070765 (17:32g)
  • [5] C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Die Grundlehren der math. Wissenschaften, Band 130, Springer-Verlag, New York, 1966. MR 34 #2380. MR 0202511 (34:2380)
  • [6] S. L. Sobolev, Applications of functional analysis in mathematical physics, Izdat. Leningrad. Gos. Univ., Leningrad, 1950; English transl., Transl. Math. Monographs, vol. 7, Amer. Math. Soc., Providence, R.I., 1963. MR 29 #2624. MR 0165337 (29:2624)
  • [7] L. V. Žižiašvili, Conjugate functions and trigonometric series, Izdat. Tibilis. Univ., Tibilisi, 1969. (Russian) MR 41 #5891. MR 0261275 (41:5891)
  • [8] A. Zygmund, Trigonometrical series. Vol. I, 2nd ed., Cambridge Univ. Press, New York, 1959. MR 21 #6498. MR 0076084 (17:844d)

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Keywords: Sobolev spaces, multiple Fourier series, localization, Lipschitz classes
Article copyright: © Copyright 1972 American Mathematical Society

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