Pointwise Fourier inversion and localisation in \(\mathbb{R}^n\)

DOI10.1007/BF02656490zbMath0896.42007OpenAlexW2036403319WikidataQ126226280 ScholiaQ126226280MaRDI QIDQ1384986

Fernando Soria, Anthony Carbery

Publication date: 1 October 1998

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59541

zbMATH Keywords

Fourier transformsets of divergencelocalization problemspherical inverse Fourier integrals

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Multipliers for harmonic analysis in several variables (42B15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (25)

Optimal constants and extremisers for some smoothing estimates ⋮ On the capacity of sets of divergence associated with the spherical partial integral operator ⋮ On generalized localization of Fourier inversion for distributions ⋮ Localization for Riesz means of Fourier expansions ⋮ Applications of the Funk-Hecke theorem to smoothing and trace estimates ⋮ Mizohata–Takeuchi estimates in the plane ⋮ On the dimension of divergence sets of dispersive equations ⋮ A bilinear extension inequality in two dimensions. ⋮ Generalized localization and summability almost everywhere of multiple Fourier series and integrals ⋮ A Stein conjecture for the circle ⋮ Riemann localisation on the sphere ⋮ On generalized localization of Fourier inversion associated with an elliptic operator for distributions ⋮ A NOTE ON LOCALISED WEIGHTED INEQUALITIES FOR THE EXTENSION OPERATOR ⋮ Localisation and weighted inequalities for spherical Fourier means ⋮ Average decay of the Fourier transform of measures with applications ⋮ Equiconvergence theorems for Sturm Liouville expansions and sets of divergence for Bochner Riesz means in Sobolev spaces ⋮ The generalized localization for multiple Fourier integrals ⋮ Tomography bounds for the Fourier extension operator and applications ⋮ Generalized localization for spherical partial sums of multiple Fourier series ⋮ Generalized localization for spherical partial sums of multiple Fourier series ⋮ Generalized localization principle for continuous wavelet decompositions ⋮ Riesz means of Fourier series and integrals: Strong summability at the critical index ⋮ Weighted norm inequalities for oscillatory integrals with finite type phases on the line ⋮ Sets which are not tube null and intersection properties of random measures ⋮ Randomised circular means of Fourier transforms of measures

Cites Work

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• Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an \(L^ 2\)-localisation principle
• Transference principles for radial multipliers
• Radial weights and mixed norm inequalities for the disc multiplier
• Hausdorff dimension and distance sets
• A note on spherical summation multipliers
• PROBLEMS OF LOCALIZATION AND CONVERGENCE FOR FOURIER SERIES IN FUNDAMENTAL SYSTEMS OF FUNCTIONS OF THE LAPLACE OPERATOR

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