Estimate of the \(L^{p}\)-Fourier transform norm on nilpotent Lie groups
type: Item
instance of: scholarly article
title: Estimate of the \(L^{p}\)-Fourier transform norm on nilpotent Lie groups
zbMATH Open document ID: 1016.43003
DOI: 10.1016/S0022-1236(02)00106-4
author: Ali Baklouti
author: Kais Smaoui
author: Jean Ludwig
published in: Journal of Functional Analysis
publication date: 2003-05-25T00:00:00Z
review text: Let \(G\) be a connected and simply connected nilpotent Lie group and let \(m\) be the dimension of the generic orbits. The authors prove that for \(1 <p \leq 2\) the norm of the \(L^p\) Fourier transform is equal or less than \(A_p^{\frac{2 \dim G-m}{2}}\) where \(A_p =(\frac{p^{\frac 1p}}{q^{\frac 1q}})^{\frac 12}\) is the \(n\)-root of the norm of the \(L^p\) Fourier transform of the \(n\)-dimensional additive abelian Lie group. To this end they make use of the orbit method and the estimation they obtain seems to be precise. In fact the number \(\frac{2\dim G-m}{2}\) is the dimension of the polarizing subalgebras of generic linear forms and then it is strictly greater than the dimension of the center of \(G\) if this is not abelian.
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 22E27
Mathematics Subject Classification ID: 43A15
zbMATH DE Number: 1915838
zbMATH Keywords: \(L^p\)-transform norm
zbMATH Keywords: nilpotent Lie group
zbMATH Keywords: Plancherel measure
reviewed by: Gabriela Paola Ovando
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915838