Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform

DOI10.1142/S0129167X16500191zbMath1355.43005arXiv1502.04958MaRDI QIDQ2797903

Troels Rousseau Johansen

Publication date: 1 April 2016

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.04958

zbMATH Keywords

Hankel transformHardy-Littlewood inequalityHausdorff-Young inequalitygeneralized Fourier transformHeisenberg-Pauli-Weyl uncertainty principledeformed Dunkl transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Other transforms and operators of Fourier type (43A32) Inequalities involving derivatives and differential and integral operators (26D10) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (32)

Flett potentials associated with differential-difference Laplace operators ⋮ Spectral theorems associated with the \((k,a)\)-generalized wavelet multipliers ⋮ Time-frequency analysis associated with the deformed Stockwell transform ⋮ Quantitative uncertainty principles associated with the \(k\)-generalized Stockwell transform ⋮ \(k\)-Hankel Wigner transform and its applications to the localization operators theory ⋮ \((k,a)\)-generalized wavelet transform and applications ⋮ Norm inequalities for maximal operators ⋮ Linear canonical deformed Hankel transform and the associated uncertainty principles ⋮ A new class of uncertainty principles for the \(k\)-Hankel wavelet transform ⋮ New uncertainty principles for the $(k,a)$-generalized wavelet transform ⋮ Heisenberg-type uncertainty inequalities for the Dunkl wavelet transform ⋮ Translation operator and maximal function for the \((k,1)\)-generalized Fourier transform ⋮ Time-frequency analysis of (k,a)-generalized wavelet transform and applications ⋮ On the kernel of the -Generalized fourier transform ⋮ Quantitative uncertainty principles associated with the k$$ k $$‐Hankel wavelet transform on ℝd$$ {\mathbb{R}}^d $$ ⋮ Generalized translation operator and uncertainty principles associated with the deformed Stockwell transform ⋮ Generalized convolution operator associated with the \((k, a)\)-generalized Fourier transform on the real line and applications ⋮ k-Hankel two-wavelet theory and localization operators ⋮ Harmonic analysis problems associated with the \(k\)-Hankel Gabor transform ⋮ \(k\)-Hankel Gabor transform and its applications to the theory of localization operators ⋮ A Hardy-Littlewood maximal operator for the generalized Fourier transform on \(\mathbb{R}\) ⋮ A product formula and a convolution structure for a \(k\)-Hankel transform on \(\mathbb{R}\) ⋮ Explicit formulas for the Dunkl dihedral kernel and the \((\kappa,a)\)-generalized Fourier kernel ⋮ Unnamed Item ⋮ \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory ⋮ Wavelet-multipliers analysis in the framework of the k-Laguerre theory ⋮ Dunkl-Stockwell transform and its applications to the time-frequency analysis ⋮ Modulus of continuity and modulus of smoothness related to the deformed Hankel transform ⋮ Time-frequency analysis associated with the \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) ⋮ An note on uncertainty inequalities for deformed harmonic oscillators ⋮ Weighted norm inequalities for the Opdam–Cherednik transform ⋮ Toeplitz operators associated with the deformed windowed Fourier transform

Cites Work

• The Clifford deformation of the Hermite semigroup
• Uncertainty principles for the Dunkl transform
• Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in \(L^2\)
• Besov-type spaces on R\(d\) and integrability for the Dunkl transform
• Remarks on the Hausdorff-Young inequality
• An entropy-based uncertainty principle for a locally compact abelian group
• Integral formula of the unitary inversion operator for the minimal representation of \(\text{O}(p,q)\)
• The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞)
• On the Clifford-Fourier Transform
• Classical and Multilinear Harmonic Analysis
• Inequalities for Fourier transforms
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