Fourier multipliers and group von Neumann algebras

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Title: Fourier multipliers and group von Neumann algebras
Author(s): Ruzhansky, M
Akylzhanov, R
Item Type: Journal Article
Abstract: In this paper we establish the Lp–Lq boundedness of Fourier multipliers on locally compact separable unimodular groups for the range of indices 1<p≤2≤q<∞. Our approach is based on the operator algebras techniques. The result depends on a version of the Hausdorff–Young–Paley inequality that we establish on general locally compact separable unimodular groups. In particular, the obtained result implies the corresponding Hörmander's Fourier multiplier theorem on Rn and the corresponding known results for Fourier multipliers on compact Lie groups.
Publication Date: 26-May-2016
Date of Acceptance: 17-May-2016
URI: http://hdl.handle.net/10044/1/32849
DOI: 10.1016/j.crma.2016.05.010
ISSN: 0249-6291
Publisher: Elsevier
Start Page: 766
End Page: 770
Journal / Book Title: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume: 354
Issue: 8
Copyright Statement: This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
RPG-2014-002
Keywords: Science & Technology
Physical Sciences
Mathematics
OPERATORS
SPACES
math.OA
math.OA
math.FA
43A85, 43A15 (Primary) 35S05 (Secondary)
General Mathematics
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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