SOBOLEV INEQUALITIES ON HOMOGENEOUS SPACES

被引：53

作者：

BIROLI, M ^{[1
]}

MOSCO, U ^{[1
]}

机构：

[1] UNIV ROMA LA SAPIENZA,DIPARTIMENTO MATEMAT,I-00185 ROME,ITALY

来源：

POTENTIAL ANALYSIS | 1995年 / 4卷 / 04期

关键词：

SOBOLEV SPACES; DIRICHLET FORMS; HOMOGENEOUS SPACES;

D O I：

10.1007/BF01053449

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

We consider a homogeneous space X = (X,d,m) of dimension v greater than or equal to 1 and a local regular Dirichlet form a in L(2) (X,m). We prove that if a Poincare inequality of exponent 1 less than or equal to p < v holds on every pseudo-hall B(x, R) of X, then Sobolev and Nash inequalities of any exponent q is an element of [p, v), as well as Poincare inequalities of any exponent q is an element of [p,+infinity), also hold on B(x, R).

引用

页码：311 / 324

页数：14