BV functions in abstract Wiener spaces

被引：48

作者：

Ambrosio, Luigi ^{[2
]}

Miranda, Michele, Jr. ^{[3
]}

Maniglia, Stefania ^{[1
]}

Pallara, Diego ^{[1
]}

机构：

[1] Univ Salento, Dipartimento Matemat Ennio De Giorgi, I-73100 Lecce, Italy

[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy

[3] Univ Ferrara, Dipartimento Matemat, I-44100 Ferrara, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 258卷 / 03期

关键词：

BV functions; Wiener space; Ornstein-Uhlenbeck semigroup; INEQUALITY;

D O I：

10.1016/j.jfa.2009.09.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Functions of bounded variation in an abstract Wiener space, i.e., an infinite-dimensional Banach space endowed with a Gaussian measure and a related differential structure, have been introduced by M. Fukushima and M. Hino using Dirichlet forms, and their properties have been studied with tools from analysis and stochastics. In this paper we reformulate, in an integral-geometric vein and with purely analytical tools, the definition and the main properties of BV functions, and investigate further properties. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：785 / 813

页数：29

共 25 条

[11]

Bakry D, 1996, INVENT MATH, V123, P259, DOI 10.1007/BF01232376

[12]

Bogachev V., 1998, GAUSSIAN MEASURES

[13] On the cases of equality in Bobkov's inequality and Gaussian rearrangement [J].

Carlen, EA ;

Kerce, C .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2001, 13 (01) :1-18

[14]

Da Prato G., 2006, Universitext

[15]

DAPRATO G, 1992, CR ACAD SCI I-MATH, V315, P1287

[16]

De Giorgi E., 1954, Ann. Mat. Pura Appl. (4), V36, P191, DOI [10.1007/BF02412838, DOI 10.1007/BF02412838]

[17]

DEGIORGI E, 1995, QUADERNI UMI, V39, P237

[18]

Feyel D., 1992, POTENTIAL ANAL, V1, P177, DOI DOI 10.1007/BF01789239.MR-1245885

[19] BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space [J].

Fukushima, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 174 (01) :227-249

[20] On the space of BV functions and a related stochastic calculus in infinite dimensions [J].

Fukushima, M ;

Hino, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 183 (01) :245-268

← 1 2 3 →