On the \(L^p - L^q\) norm of the Hankel transform and related operators

DOI10.1016/j.jmaa.2008.06.053zbMath1153.44002OpenAlexW2069605916MaRDI QIDQ947572

Laura De Carli

Publication date: 6 October 2008

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.06.053

zbMATH Keywords

Hankel transformLaguerre polynomialsBessel functionsconvolution operatorFourier-Bessel transformbest constants

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items (16)

Inequalities related to spherical harmonics associated with the Weinstein operator ⋮ FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES ⋮ Sharp Pitt's inequality and Beckner's logarithmic uncertainty principle for the Weinstein transform ⋮ Pitt's inequality and logarithmic uncertainty principle for the Clifford-Fourier transform ⋮ The generalized Kontorovich-Lebedev transform and associated operators ⋮ Weighted Fourier inequalities: Boas' conjecture in \({\mathbb{R}}^{n}\) ⋮ Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in \(L^2\) ⋮ Weighted norm inequalities for integral transforms ⋮ Continuous Bessel wavelet transform of distributions ⋮ Sharp Shannon's and logarithmic Sobolev inequalities for the Hankel transform ⋮ Pitt and Boas inequalities for Fourier and Hankel transforms ⋮ Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates ⋮ Uniform convergence of Hankel transforms ⋮ Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions ⋮ On the Hankel transform of functions from Nikol'ski type classes ⋮ The Boas problem on Hankel transforms

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• Gaussian kernels have only Gaussian maximizers
• The hypercontractive approach to exactly bounding an operator with complex Gaussian kernel
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• Interpolation of Operators with Change of Measures
• An Example in the Theory of Hypercontractive Semigroups
• Equiconvergence Theorems for Fourier-Bessel Expansions with Applications to the Harmonic Analysis of Radial Functions in Euclidean and Noneuclidean Spaces
• Mean Convergence of Expansions in Laguerre and Hermite Series

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