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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the localization of rectangular partial sums for multiple Fourier series
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by Fon Che Liu PDF
Proc. Amer. Math. Soc. 34 (1972), 90-96 Request permission


The question of the localization for rectangular partial sums of the multiple Fourier series for functions of Sobolev spaces is settled.
    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.
  • Casper Goffman and Fon-che Liu, On the localization property of square partial sums for multiple Fourier series, Studia Math. 44 (1972), 61–69. MR 312147, DOI 10.4064/sm-44-1-61-69
  • V. A. Il′in, Localization and convergence problems for Fourier series in fundamental function systems of Laplace’s operator, Uspehi Mat. Nauk 23 (1968), no. 2 (140), 61–120 (Russian). MR 0223823
  • B. M. Levitan, On summability of multiple series and Fourier integrals, Dokl. Akad. Nauk SSSR (N.S.) 102 (1955), 1073–1076 (Russian). MR 0070765
  • Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511
  • S. L. Sobolev, Applications of functional analysis in mathematical physics, Translations of Mathematical Monographs, Vol. 7, American Mathematical Society, Providence, R.I., 1963. Translated from the Russian by F. E. Browder. MR 0165337
  • L. V. Žižiašvili, Sopryazhennye funktsii i trigonometricheskie ryady, Izdat. Tbilis. Univ., Tbilisi, 1969 (Russian). MR 0261275
  • Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. MR 0076084
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 90-96
  • MSC: Primary 42A92; Secondary 42A62
  • DOI:
  • MathSciNet review: 0294993