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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 26, Issue 2


On the norm of the Lp-Fourier transform on compact extensions of ℝn

Ali Baklouti / Junko Inoue
Published Online: 2012-02-03 | DOI: https://doi.org/10.1515/forum-2011-0094


This paper aims to prove that the norm of the Lp-Fourier transform of the semidirect product nK is Apn, where 1<p2, q=p/(p-1), Ap=p12pq-12q, and K stands for a compact subgroup of automorphisms of ℝn. An extremal function is given by an extension of a Gaussian function. Besides, as an example of non-compact extension, the universal covering group of the Euclidean motion group of the plane is also treated and an estimate of the norm is obtained.

Keywords: Hausdorff–Young inequality; unitary representations of Lie groups; compact extension; Fourier transform norm; Plancherel formula

MSC: 22E30; 43A30; 43A80

About the article

Received: 2011-09-08

Revised: 2012-01-09

Published Online: 2012-02-03

Published in Print: 2014-03-01

Funding Source: Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science

Award identifier / Grant number: 21540180

Funding Source: Representations of Lie groups and special functions

Award identifier / Grant number: DGRST 00UR1501

Citation Information: Forum Mathematicum, Volume 26, Issue 2, Pages 621–636, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2011-0094.

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