On Fundamental Solutions of Generalized Schrödinger Operators

✍ Scribed by Zhongwei Shen

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 268 KB
• Volume: 167
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1999.3455

✦ Synopsis

We consider the generalized Schro dinger operator &2++, where + is a nonnegative Radon measure in R n , n 3. Assuming that + satisfies certain scale-invariant Kato conditions and doubling conditions we establish the following bounds for the fundamental solution of &2++ in R n ,

where d(x, y, +) is the distance function for the modified Agmon metric m(x, +) dx 2 associated with +. We also study the boundedness of the corresponding Riesz transforms {(&2++) &1Â2 on L p (R n , dx).