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Matematicheskie Zametki, 2016, Volume 100, Issue 1, Pages 109–117
DOI: https://doi.org/10.4213/mzm11127 (Mi mzm11127) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

E. R. Liflyand

Bar-Ilan University, Israel
Full-text PDF (463 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11127
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.
Received: 02.09.2015
English version:
Mathematical Notes, 2016, Volume 100, Issue 1, Pages 93–99
DOI: https://doi.org/10.1134/S0001434616070087
Bibliographic databases:
Document Type: Article
UDC: 517.518.5
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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