Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / 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

Online
ISSN
1435-5337
See all formats and pricing
More options …
Volume 26, Issue 2

Issues

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

Abstract

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.

Export Citation

© 2015 by De Gruyter.Get Permission

Comments (0)

Please log in or register to comment.
Log in