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Estimates for the Growth Order of Sequences of Multiple Rectangular Fourier Sums of Integrable Functions

Abstract

Estimates on the growth order of sequences of rectangular partial sums of multiple Fourier series of functions integrable on the d-dimensional torus [−π, π]d are obtained.

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Correspondence to N. Yu. Antonov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 3–15, 2013.

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Antonov, N.Y. Estimates for the Growth Order of Sequences of Multiple Rectangular Fourier Sums of Integrable Functions. J Math Sci 209, 1–11 (2015). https://doi.org/10.1007/s10958-015-2481-7

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Keywords

  • Fourier Series
  • Nondecreasing Function
  • Arbitrary Sequence
  • Nondecreasing Sequence
  • Growth Order