Poincare type inequalities on the discrete cube and in the CAR algebra

• 成果类型: Article
• 署名作者: Ben Efraim, L.; Lust-Piquard, F.
• 署名单位: Hebrew University of Jerusalem; Weizmann Institute of Science; CY Cergy Paris Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0094-x
• 发表日期: 2008
• 页码: 569-602
• 关键词: spaces; khintchine

摘要

We prove L-p Poincare inequalities with suitable dimension free constants for functions on the discrete cube {- 1, 1}(n). As well known, such inequalities for p an even integer allow to recover an exponential inequality hence the concentration phenomenon first obtained by Bobkov and Gotze. We also get inequalities between the L-p norms of vertical bar|del f | and del(alpha) f, alpha > 0; moreover L-p spaces may be replaced by more general ones. Similar results hold true, replacing functions on the cube by matrices in the *-algebra spanned by n fermions and the L-p norm by the Schatten norm C-p.