On Lp Liouville Theorems for Dirichlet Forms

被引：2

作者：

Hua, Bobo ^{[1
,2
]}

Keller, Matthias ^{[3
]}

Lenz, Daniel ^{[4
]}

Schmidt, Marcel ^{[5
]}

机构：

[1] Fudan Univ, LMNS, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Shanghai Ctr Math Sci, Jiangwan Campus,2005 Songhu Rd, Shanghai 200438, Peoples R China

[3] Univ Potsdam, Inst Math, D-14476 Potsdam, Germany

[4] Friedrich Schiller Univ Jena, Inst Math, D-07743 Jena, Germany

[5] Univ Leipzig, Math Inst, D-04109 Leipzig, Germany

来源：

DIRICHLET FORMS AND RELATED TOPICS: IN HONOR OF MASATOSHI FUKUSHIMA'S BEIJU (IWDFRT 2022) | 2022年 / 394卷

关键词：

Dirichlet forms; Liouville property; Superharmonic functions; HARMONIC-FUNCTIONS;

D O I：

10.1007/978-981-19-4672-1_12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima's ergodic theorem for the harmonic functions in the domain of the L-p generator. Secondly we prove analogues of Yau's and Karp's Liouville theorems for weakly harmonic functions. Both say that weakly harmonic functions which satisfy certain L-p growth criteria must be constant. As consequence we give an integral criterion for recurrence.

引用

页码：201 / 221

页数：21

共 16 条

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[3]

Davies E.B., 1989, CAMBRIDGE TRACTS MAT, V92

[4]

Dellacherie C., 1980, Actualites Scientifiques et Industrielles, V1385