The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds

• 成果类型: Article
• 署名作者: Hofmann, S; Lacey, M; McIntosh, A
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597200
• 发表日期: 2002
• 页码: 623-631
• 关键词: square-root problem

摘要

We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis. we establish that the domain of the square root of a complex uniformly elliptic operator L = -div(Adel) with bounded measurable coefficients in R-n is the Sobolev space H-1(R-n) in any dimension with the estimate parallel torootLfparallel to(2) - parallel todelfparallel to(2). We note, in particular, that for such operators, the Gaussian hypothesis holds always in two dimensions.