Functional inequalities for time-changed symmetric α-stable processes

被引：1

作者：

Wang, Jian ^{[1
,2
,3
]}

Zhang, Longteng ^{[4
,5
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Peoples R China

[2] Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat FJKLMAA, Fuzhou 350007, Peoples R China

[3] Fujian Normal Univ, Ctr Appl Math Fujian Prov FJNU, Fuzhou 350007, Peoples R China

[4] Fujian Normal Univ, Concord Univ Coll, Fuzhou 350007, Peoples R China

[5] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2021年 / 16卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Symmetric α -stable process; time change; functional inequality;

D O I：

10.1007/s11464-021-0908-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish sharp functional inequalities for time-changed symmetric alpha-stable processes on Double-struck capital R-d with d > 1 and alpha is an element of (0, 2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x) = (1 + divide x divide )(beta) with beta > alpha, we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.

引用

页码：595 / 622

页数：28

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