Asymptotics of the Fourier sine transform of a function of bounded variation

DOI10.1134/S0001434616070087zbMath1362.42013MaRDI QIDQ509049

Elijah Liflyand

Publication date: 8 February 2017

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Fourier transformHardy spaceHilbert transformfunction of bounded variationHardy inequalitylocally absolutely continuous functionM. Riesz theorem

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Hardy spaces (30H10)

Related Items (1)

The Fourier transform of a function of bounded variation: symmetry and asymmetry

Cites Work

• Weighted Paley-Wiener theorem on the Hilbert transform
• On asymptotics of Fourier transform for functions of certain classes
• The Banach algebra \(A^*\) and its properties
• Interpolation properties of a scale of spaces
• Fourier transform versus Hilbert transform
• On inequalities for the Fourier transform of functions from Lorentz spaces
• On the spectral synthesis of bounded functions
• Interaction between the Fourier transform and the Hilbert transform
• The Fourier Transforms of General Monotone Functions
• Multiple Fourier transforms and trigonometric series in line with Hardy’s variation
• Some Elementary Inequalities for Integrals with Applications to Fourier Transforms
• ON INTEGRAL NORMS FOR POLYNOMIALS
• Decay of the Fourier Transform
• Linear Functionals Connected with Strong Cesàro Summability
• A note on Hilbert’s operator
• A class of trigonometric series
• Hardy spaces generated by an integrability condition
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