Super-Poincar, and Nash-type inequalities for subordinated semigroups

被引：4

作者：

Gentil, Ivan ^{[1
]}

Maheux, Patrick ^{[2
]}

机构：

[1] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

[2] Univ Orleans, Dept Math, Federat Denis Poisson, F-45067 Orleans 2, France

来源：

SEMIGROUP FORUM | 2015年 / 90卷 / 03期

关键词：

Super-Poincare inequality; Nash-type inequality; Symmetric semigroup; Subordination in the sense of Bochner; Bernstein function; Super-Poincare profile; FUNCTIONAL INEQUALITIES;

D O I：

10.1007/s00233-014-9648-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if a super-Poincar, inequality is satisfied by an infinitesimal generator of a symmetric contraction semigroup on and that is contracting on , then it implies a corresponding super-Poincar, inequality for for any Bernstein function . We also study the converse of this statement. We prove similar results for Nash-type inequalities. We apply our results to Euclidean, Riemannian, hypoelliptic and Ornstein-Uhlenbeck settings.

引用

页码：660 / 693

页数：34

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