Riesz transforms and Lie groups of polynomial growth

Authors
ter Elst, AFM Robinson, DW Sikora, A
Citation
Afm. Ter Elst et al., Riesz transforms and Lie groups of polynomial growth, J FUNCT ANA, 162(1), 1999, pp. 14-51
Citations number
20
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN journal
00221236 → ACNP
Volume
162
Issue
1
Year of publication
1999
Pages
14 - 51
Database
ISI
SICI code
0022-1236(19990220)162:1<14:RTALGO>2.0.ZU;2-V
Abstract
Let G be a Lie group of polynomial growth. We prove that the second-order R iesz transforms on L-2(G; dg) are bounded if; and only if, the group is a d irect product of a compact group and a nilpotent group, in which case the t ransforms of all orders are bounded. (C) 1999 Academic Press.