$L^p$-bounds for pseudo-differential operators on compact Lie groups

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Title: $L^p$-bounds for pseudo-differential operators on compact Lie groups
Authors: Delgado Valencia, JC
Ruzhansky, M
Item Type: Journal Article
Abstract: Given a compact Lie group G, in this paper we establish Lp-bounds for pseudo-di erential operators in Lp(G). The criteria here are given in terms of the concept of matrix symbols de ned on the non-commutative analogue of the phase space G x Ĝ, where G is the unitary dual of Ĝ. We obtain two di erent types of Lpbounds: rst for nite regularity symbols and second for smooth symbols. The conditions for smooth symbols are formulated using Sm ;(G) classes which are a suitable extension of the well known (p,δ) ones on the Euclidean space. The results herein extend classical Lpbounds established by C. Fe erman on Rn.
Issue Date: 3-Apr-2017
Date of Acceptance: 14-Jan-2017
URI: http://hdl.handle.net/10044/1/43750
DOI: https://dx.doi.org/10.1017/S1474748017000123
ISSN: 1474-7480
Publisher: Cambridge University Press (CUP)
Journal / Book Title: Journal of the Institute of Mathematics of Jussieu
Copyright Statement: © Cambridge University Press 2017. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi:10.1017/S1474748017000123
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
Keywords: math.AP
Primary 35S05, Secondary 22E30, 47G30
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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