The Poincare inequality is an open ended condition

• 成果类型: Article
• 署名作者: Keith, Stephen; Zhong, Xiao
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.167.575
• 发表日期: 2008
• 页码: 575-599
• 关键词: sobolev spaces; potential-theory; removable sets; REGULARITY

摘要

Let p > 1 and let (X, d, mu) be a complete metric measure space with mu Borel and doubling that admits a (1, p)-Poincare inequality. Then there exists epsilon > 0 such that (X, d, mu) admits a, (1, q)-Poincare inequality for every q > p - epsilon, quantitatively.