Dirichlet spaces on H-convex sets in Wiener space

被引：11
|
作者：
Hino, Masanori [1 ]
机构：
[1] Kyoto Univ, Grad Sch Informat, Kyoto 6068501, Japan
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2011年 / 135卷 / 6-7期
关键词：
Dirichlet space; Convex set; Wiener space; RADEMACHERS THEOREM; BV FUNCTIONS; FORMS;
D O I：
10.1016/j.bulsci.2011.07.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the (1, 2)-Sobolev space W-1,W-2(U) on subsets U in an abstract Wiener space, which is regarded as a canonical Dirichlet space on U. We prove that W-1,W-2 (U) has smooth cylindrical functions as a dense subset if U is H-convex and H-open. For the proof, the relations between H-notions and quasi-notions are also studied. (C) 2011 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：667 / 683
页数：17
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