Weighted Fourier inequalities: Boas' conjecture in \({\mathbb{R}}^{n}\)

DOI10.1007/S11854-011-0013-ZzbMath1246.42011OpenAlexW2045391808WikidataQ123301699 ScholiaQ123301699MaRDI QIDQ415765

Elijah Liflyand, Sergey Yu. Tikhonov, Dmitry Gorbachev

Publication date: 9 May 2012

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-011-0013-z

zbMATH Keywords

Fourier transformradial functionBoas' conjecture

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Inequalities for sums, series and integrals (26D15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (22)

Functions with general monotone Fourier coefficients ⋮ A new generalization of Boas theorem for some Lorentz spaces Λ_q(ω) ⋮ Hardy-Littlewood and Pitt's inequalities for Hausdorff operators ⋮ Bourgain-Brezis-Mironescu-Maz'ya-Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation ⋮ Transformation of Fourier series by means of general monotone sequences ⋮ Fourier transforms of convolutions of functions in Lebesgue and Lorentz spaces ⋮ Sparse grid approximation in weighted Wiener spaces ⋮ Sharp approximation theorems and Fourier inequalities in the Dunkl setting ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Weighted norm inequalities for integral transforms ⋮ Growth and integrability of Fourier transforms on Euclidean space ⋮ Pitt and Boas inequalities for Fourier and Hankel transforms ⋮ Asymptotic decay of Fourier, Laplace and other integral transforms ⋮ Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates ⋮ Uniform convergence of Hankel transforms ⋮ Functions preserving general monotone sequence ⋮ Unnamed Item ⋮ Decay of Fourier Transforms and Generalized Besov Spaces ⋮ The Boas problem on Hankel transforms ⋮ Hardy-Littlewood-type theorems for Fourier transforms in \(\mathbb{R}^d\) ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

Cites Work

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• Interpolation of Linear Operators
• Some Weighted Norm Inequalities for the Fourier Transform of Functions With Vanishing Moments
• Weighted Fourier Transform Inequalities for Radially Decreasing Functions
• Hardy Inequalities with Mixed Norms
• Weighted Norm Estimates for the Fourier Transform with a Pair of Weights
• Pitt's Inequality and the Uncertainty Principle
• Pitt's inequality with sharp convolution estimates
• The integrability class of the sine transform of a monotonic function

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