Singular integral operator, Hardy–Morrey space estimates for multilinear operators and Navier–Stokes equations

✍ Scribed by Henggeng Wang; Houyu Jia

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 344 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1275

✦ Synopsis

After establishing the molecule characterization of the Hardy-Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy-Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier-Stokes equations for the initial data in the Hardy-Morrey space HM p q (p n) for q as small as possible.

Here, the Hardy-Morrey space estimates for multilinear operators are important tools.