A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes

被引：37

作者：

Bañuelos, R

Latala, R

Méndez-Hernández, PJ

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Warsaw Univ, Inst Math, PL-02097 Warsaw, Poland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 10期

关键词：

symmetric stable processes; generalized isoperimetric inequalities; inradius;

D O I：

10.1090/S0002-9939-01-06137-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive an inequality for multiple integrals from which we conclude various generalized isoperimetric inequalities for Brownian motion and symmetric stable processes in convex domains of fixed inradius. Our multiple integral inequality is a replacement for the classical inequality of H. J. Brascamp, E. H. Lieb and J. M. Luttinger, where instead of fixing the volume of the domain one fixes its inradius.

引用

页码：2997 / 3008

页数：12

共 18 条

[1]

Bandle C., 1980, MONOGR STUD MATH, V7

[2]

Banuelos R, 1997, INDIANA U MATH J, V46, P83

[3]

Banuelos R, 1995, MICH MATH J, V42, P603

[4] BROWNIAN-MOTION AND THE FUNDAMENTAL-FREQUENCY OF A DRUM [J].

BANUELOS, R ;

CARROLL, T .

DUKE MATHEMATICAL JOURNAL, 1994, 75 (03) :575-602

[5]

Blumenthal R., 1960, Trans. Amer. Math. Soc., V95, P263, DOI DOI 10.1090/S0002-9947-1960-0119247-6

[6]

Brascamp H.J., 1974, J FUNCT ANAL, V17, P227, DOI [10.1016/0022-1236(74)90013-5, DOI 10.1016/0022-1236(74)90013-5]

[7] Estimates on Green functions and Poisson kernels for symmetric stable processes [J].

Chen, ZQ ;

Song, RM .

MATHEMATISCHE ANNALEN, 1998, 312 (03) :465-501

[8] Intrinsic ultracontractivity and conditional gauge for symmetric stable processes [J].

Chen, ZQ ;

Song, RM .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 150 (01) :204-239

[9]

Davies EB., 1989, HEAT KERNELS SPECTRA, DOI 10.1017/CBO9780511566158

[10]

Getoor RK., 1961, Trans Am Math Soc, V101, P75, DOI [DOI 10.2307/1993412, DOI 10.1090/S0002-9947-1961-0137148-5]

← 1 2 →