Estimate of the \(L^{p}\)-Fourier transform norm on nilpotent Lie groups

DOI10.1016/S0022-1236(02)00106-4zbMath1016.43003MaRDI QIDQ1874703

Ali Baklouti, Jean Ludwig, Kais Smaoui

Publication date: 25 May 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

Plancherel measurenilpotent Lie group\(L^p\)-transform norm

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Other transforms and operators of Fourier type (43A32) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (16)

Hardy's theorem for Gabor transform on nilpotent Lie groups ⋮ Estimate of the \(L^p\)-Fourier transform norm on strong \(\ast\)-regular exponential solvable Lie groups ⋮ Heisenberg–Pauli–Weyl inequality for connected nilpotent Lie groups ⋮ An \(L^p\)-\(L^q\) analog of Miyachi's theorem for nilpotent Lie groups and sharpness problems ⋮ An inequality for the convolutions on unimodular locally compact groups and the optimal constant of Young's inequality ⋮ The \(L^{p}-L^{q}\) analog of Morgan's theorem on exponential solvable Lie groups ⋮ VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS ⋮ Inequalities and local uncertainty principles for nilpotent Lie groups ⋮ Heisenberg uncertainty inequality for certain Lie groups ⋮ On theorems of Morgan and Cowling-Price for selected nilpotent Lie groups ⋮ Estimate of the Lp -Fourier transform norm for connected nilpotent Lie groups ⋮ The \(L^p\)-Fourier transform norm on compact extensions of locally compact groups ⋮ Weyl transform and generalized spectrogram associated with quaternion Heisenberg group ⋮ The Lp –Lq version of Hardy's Theorem on nilpotent Lie groups ⋮ Uncertainty Principle for Gabor Transform on the Quaternionic Heisenberg Group ⋮ Heisenberg uncertainty inequality for Gabor transform on nilpotent Lie groups

Cites Work

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• \(L^ p\)-Fourier transforms on nilpotent Lie groups and solvable Lie groups acting on Siegel domains
• Inequalities in Fourier analysis
• On the Hausdorff-Young theorem for integral operators
• \(L^p\) Fourier transformation on non-unimodular locally compact groups
• L p Fourier Transforms on Locally Compact Unimodular Groups
• The Norm of the L p -Fourier Transform on Unimodular Groups
• The Norm of the L^p-Fourier Transform, II
• Sharpness in Young’s inequality for convolution
• Abstract Interpolation and Operator-Valued Kernels
• Uniform convergence and decay of Fourier series on compact nilmanifolds

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