dc.contributor.author | Delgado, J | en_US |
dc.contributor.author | Ruzhansky, M | en_US |
dc.date.accessioned | 2018-11-22T15:47:14Z | |
dc.date.submitted | 2018-11-22T14:29:06.801Z | |
dc.identifier.other | 10.1017/S1474748017000123 | |
dc.identifier.uri | https://doi.org/10.1017/S1474748017000123 | |
dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/52983 | |
dc.description | 29 pages; a section on motivation and applications is added; to appear in J. Inst. Math. Jussieu | en_US |
dc.description | 29 pages; a section on motivation and applications is added; to appear in J. Inst. Math. Jussieu | |
dc.description | 29 pages; a section on motivation and applications is added; to appear in J. Inst. Math. Jussieu | en_US |
dc.description.abstract | Given a compact Lie group $G$, in this paper we establish $L^p$-bounds for pseudo-differential operators in $L^p(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the non-commutative analogue of the phase space $G\times\widehat{G}$, where $\widehat{G}$ is the unitary dual of $G$. We obtain two different types of $L^p$ bounds: first for finite regularity symbols and second for smooth symbols. The conditions for smooth symbols are formulated using $\mathscr{S}_{\rho,\delta}^m(G)$ classes which are a suitable extension of the well known $(\rho,\delta)$ ones on the Euclidean space. The results herein extend classical $L^p$ bounds established by C. Fefferman on $\mathbb R^n$. While Fefferman's results have immediate consequences on general manifolds for $\rho>\max\{\delta,1-\delta\}$, our results do not require the condition $\rho>1-\delta$. Moreover, one of our results also does not require $\rho>\delta$. Examples are given for the case of SU(2)$\cong\mathbb S^3$ and vector fields/sub-Laplacian operators when operators in the classes $\mathscr{S}_{0,0}^m$ and $\mathscr{S}_{\frac12,0}^m$ naturally appear, and where conditions $\rho>\delta$ and $\rho>1-\delta$ fail, respectively. | en_US |
dc.language.iso | en | en_US |
dc.rights | Creative Commons Attribution | |
dc.subject | math.AP | en_US |
dc.subject | math.AP | en_US |
dc.subject | Primary 35S05, Secondary 22E30, 47G30 | en_US |
dc.title | $L^p$-bounds for pseudo-differential operators on compact Lie groups | en_US |
dc.type | Article | |
dc.rights.holder | Cambridge University Press 2017 | |
pubs.author-url | http://arxiv.org/abs/1605.07027v2 | en_US |
pubs.notes | Not known | en_US |