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 Mat. Zametki, 2016, Volume 100, Issue 1, Pages 109–117 (Mi mz11127)

Asymptotics of the Fourier Sine Transform of a Function of Bounded Variation

E. R. Liflyand

Bar-Ilan University, Israel

Abstract: For the asymptotic formula for the Fourier sine transform of a function of bounded variation, we find a new proof entirely within the framework of the theory of Hardy spaces, primarily with the use of the Hardy inequality. We show that, for a function of bounded variation whose derivative lies in the Hardy space, every aspect of the behavior of its Fourier transform can somehow be expressed in terms of the Hilbert transform of the derivative.

Keywords: function of bounded variation, Fourier transform, locally absolutely continuous function, Hilbert transform, Hardy space, Hardy inequality, M. Riesz theorem.

DOI: https://doi.org/10.4213/mzm11127

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English version:
Mathematical Notes, 2016, 100:1, 93–99

Bibliographic databases:

UDC: 517.518.5

Citation: E. R. Liflyand, “Asymptotics of the Fourier Sine Transform of a Function of Bounded Variation”, Mat. Zametki, 100:1 (2016), 109–117; Math. Notes, 100:1 (2016), 93–99

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz11127
• https://doi.org/10.4213/mzm11127
• http://mi.mathnet.ru/eng/mz/v100/i1/p109

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. Liflyand, “The Fourier transform of a function of bounded variation: symmetry and asymmetry”, J. Fourier Anal. Appl., 24:2 (2018), 525–544
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