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.
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页码：660 / 693
页数：34
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