Nash type inequalities for fractional powers of non-negative self-adjoint operators

被引：34

作者：

Bendikov, Alexander

Maheux, Patrick

机构：

[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 359卷 / 07期

关键词：

Nash inequality; fractional powers of operators; semigroup of operators; logarithmic Sobolev inequality; ultracontractivity property; Dirichlet form;

D O I：

10.1090/S0002-9947-07-04020-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator A, we prove a Nash type inequality for the fractional powers A(alpha) of A. Under some assumptions, we give ultracontractivity bounds for the semigroup (T-t,T-alpha) generated by -A(alpha).

引用

页码：3085 / 3097

页数：13