Geodesic
Asymptotics of the Fourier Sine Transform of a~Function of Bounded Variation
Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 109-117

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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, locally absolutely continuous function, Hardy space, Hardy inequality, M. Riesz theorem.
Mots-clés : Fourier transform, Hilbert transform 
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     author = {E. R. Liflyand},
     title = {Asymptotics of the {Fourier} {Sine} {Transform} of {a~Function} of {Bounded} {Variation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {109--117},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a7/}
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E. R. Liflyand. Asymptotics of the Fourier Sine Transform of a~Function of Bounded Variation. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 109-117. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a7/