Weights of holomorphic extension and restriction

详细信息	查看全文 | 推荐本文 |

• 作者：Diederich ; K. ; Herbort ; G. ; Michel ; V.
• 刊名：Journal des Mathematiques Pures et Appliquees
• 出版年：1998
• 期刊代码：29_00217824
• 类别：mt
• 出版时间：September, 1998
• 卷：77
• 期：7
• 页码：697-719
• 文件大小：804 K

摘要

Let D center border=0 SRC=/images/glyphs/BOC.GIF>center border=0 SRC=/images/glyphs/BOC.GIF> Cⁿ be a domain and D′ center border=0 SRC=/images/glyphs/BOC.GIF> D a closed complex submanifold. A normalized weight function center border=0 SRC=/images/glyphs/CD4.GIF> on D′ is called weight of restriction, if the restriction of any L²-holomorphic function f on D to D′ is contained in L²(D′, center border=0 SRC=/images/glyphs/CD4.GIF>), and it is called a weight of extension, if any holomorphic function in L²(D′, center border=0 SRC=/images/glyphs/CD4.GIF>) can be extended to a L²-holomorphic function on D. Properties of the families of weights of restriction and weights of extension and relations between them are studied in this article. An application to the boundary behavior of the Bergman metric is given.