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Localization and summability of multiple fourier series

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Acta Mathematica

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References

  1. H. Batemanet al., Higher Transcendental Functions, Vol. 2. New York, 1953.

  2. H. Bateman,et al. Tables of Integral Transforms, Vol. 2. New York, 1954.

  3. S. Bochner, Summation of multiple Fourier series by spherical means.Trans. Amer. Math. Soc., 40 (1936), 175–207.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Bochner &K. Chandrasekharan, On the localization property of multiple Fourier series.Ann. of Math. 49 (1948), 966–978.

    Article  MathSciNet  Google Scholar 

  5. S. Bochner & K. Chandrasekharan,Fourier Transforms. Princeton, 1949.

  6. K. Chandrasekharan & S. Minakshisundaram,Typical Means. Bombay, 1952.

  7. A. L. Dixon &W. L. Ferrar, Some summations over lattice points of a circle. II.Quart. J. Math. Oxford, 5 (1934), 172–185.

    Article  Google Scholar 

  8. C. Fox, The asymptotic expansion of generalized hypergeometric functions.Proc. London Math. Soc. (2), 27 (1928), 389–400.

    Article  Google Scholar 

  9. S. Kaczmarz & H. Steinhaus,Theorie der Orthogonalreihen. Warsaw. 1935.

  10. S. Minakshisundaram, Notes on Fourier expansions III,Amer. J. Math. (71), 1949, 60–66.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Mitchell. Summability of multiple orthogonal series.Trans. Amer. Math. Soc., 71 (1951), 136–151.

    Article  MATH  MathSciNet  Google Scholar 

  12. K. T. Smith, A generalization of an inequality of Hardy and Littlewood.Canadian J. Math., 8 (1956), 157–170.

    MATH  Google Scholar 

  13. E. M. Stein, Interpolation of linear operators.Trans. Amer. Math. Soc., 83 (1956), 482–492.

    Article  MATH  MathSciNet  Google Scholar 

  14. E. C. Titchmarsh, Additional note on conjugate functions.London Math. Soc., 5 (1929), 204–206.

    Article  Google Scholar 

  15. A. Zygmund,Trigonometrical Series. Warsaw, 1935.

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This research was supported by the United States Air Force under Contract No. AF 49 (638)-42, monitored by the AF Office of Scientific Research of the Air Research and Development Command.

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Stein, E.M. Localization and summability of multiple fourier series. Acta Math. 100, 93–147 (1958). https://doi.org/10.1007/BF02559603

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