Functional inequalities for time-changed symmetric α-stable processes

doi:10.1007/s11464-021-0908-7

Frontiers of Mathematics in China

2021, Vol. 16

Issue (2): 595-622 https://doi.org/10.1007/s11464-021-0908-7

本期目录

Functional inequalities for time-changed symmetric

α

-stable processes

Jian WANG¹(

), Longteng ZHANG²

¹. College of Mathematics and Informatics & Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA) & Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou 350007, China
². Concord University College & College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350007, China

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Abstract：

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

Key words： α-stable process')" href="#">Symmetric

α

-stable process time change, functional inequality

收稿日期: 2020-06-30 出版日期: 2021-06-01

Corresponding Author(s): Jian WANG

引用本文:

. [J]. Frontiers of Mathematics in China, 2021, 16(2): 595-622.
Jian WANG, Longteng ZHANG. Functional inequalities for time-changed symmetric

α

-stable processes. Front. Math. China, 2021, 16(2): 595-622.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-021-0908-7
https://academic.hep.com.cn/fmc/CN/Y2021/V16/I2/595

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