The Resolvent Problem and $${{H^{infty}}}$$-calculus of the Stokes Operator in Unbounded Cylinders with Several Exits to Infinity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The Resolvent Problem and $${{H^{infty}}}$$-calculus of the Stokes Operator in Unbounded Cylinders with Several Exits to Infinity

Authors:	Reinhard Farwig Ri Myong-Hwan

Affiliation:	(1) Department of Mathematics, Darmstadt University of Technology, 64289 Darmstadt, Germany;(2) Institute of Mathematics, Academy of Sciences, Pyongyang, DPR Korea

Abstract:	It is proved that the Stokes operator in L^q -space on an infinite cylindrical domain of ${{mathbb{R}^{n}}}$ , , with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded ${{H^{infty}}}$ -calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight cylinder with bounded cross-section is studied in L ^q ${{(mathbb{R}; L^{r}_{omega} (Sigma))}}$ where and ${{omega , epsilon , A_{r}(mathbb{R}^{n-1})}}$ is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on -boundedness of operator families and on square function estimates involving Muckenhoupt weights.

Keywords:	KeywordHeading" >: IEq10" > /content/d22234x502075q72/28_2007_Article_300_TeX2GIFIEq10.gif" alt=" $${{H^{infty}}}$$ " align=" middle" border=" 0" > -calculus Stokes operator Stokes resolvent estimate Stokes semigroup unbounded cylindrical domains Muckenhoupt weights
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