Extended solution of Boas' conjecture on Fourier transforms

DOI10.1016/j.crma.2008.07.029zbMath1151.42002OpenAlexW2036701230WikidataQ122966160 ScholiaQ122966160MaRDI QIDQ957552

Elijah Liflyand, Sergey Yu. Tikhonov

Publication date: 28 November 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.07.029

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (23)

Uniform convergence and integrability of Fourier integrals ⋮ Functions with general monotone Fourier coefficients ⋮ A new generalization of Boas theorem for some Lorentz spaces Λ_q(ω) ⋮ Hardy-type theorems on Fourier transforms revised ⋮ On spectral properties of the modified convolution operator ⋮ Weighted integrability of multiplicative Fourier transforms ⋮ Uniform convergence of double sine transforms of general monotone functions ⋮ Uniform convergence and integrability of multiplicative Fourier transforms ⋮ General monotonicity and interpolation of operators ⋮ Weighted Fourier inequalities: Boas' conjecture in \({\mathbb{R}}^{n}\) ⋮ Fourier transforms of convolutions of functions in Lebesgue and Lorentz spaces ⋮ Net spaces and boundedness of integral operators ⋮ Unnamed Item ⋮ Weighted norm inequalities for integral transforms ⋮ A concept of general monotonicity and applications ⋮ Pitt and Boas inequalities for Fourier and Hankel transforms ⋮ Asymptotic decay of Fourier, Laplace and other integral transforms ⋮ General monotone functions and their Fourier coefficients ⋮ Rearrangements of general monotone functions and of their Fourier transforms ⋮ Uniform convergence of Hankel transforms ⋮ Unnamed Item ⋮ On Leray’s Formula ⋮ The Boas problem on Hankel transforms

Cites Work

• Unnamed Item
• Trigonometric series with general monotone coefficients
• Best approximation and moduli of smoothness: Computation and equivalence theorems
• Integrability conditions for the Fourier transform
• Weighted Fourier inequalities: New proofs and generalizations.
• Integrability theorems for Fourier series
• Convergence of trigonometric series with general monotone coefficients
• The Fourier Transforms of General Monotone Functions
• Some Weighted Norm Inequalities for the Fourier Transform of Functions With Vanishing Moments
• Hardy Inequalities with Mixed Norms
• The integrability class of the sine transform of a monotonic function

This page was built for publication: Extended solution of Boas' conjecture on Fourier transforms