Dirichlet heat kernel estimates for rectilinear stable processes

Zhen Qing Chen; Eryan Hu; Guohuan Zhao

doi:10.1016/j.jfa.2024.110812

Dirichlet heat kernel estimates for rectilinear stable processes

Zhen Qing Chen^*, Eryan Hu, Guohuan Zhao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let d≥2, α∈(0,2), and X be the rectilinear α-stable process on R^d. We first present a geometric characterization of open subset D⊂R^d so that the part process X^D of X in D is irreducible. We then study the properties of the transition density functions of X^D, including the strict positivity property as well as their sharp two-sided bounds in C^1,1 domains in R^d. Our bounds are shown to be sharp for a class of C^1,1 domains.

Original language	English
Article number	110812
Journal	Journal of Functional Analysis
Volume	288
Issue number	6
DOIs	https://doi.org/10.1016/j.jfa.2024.110812
Publication status	Published - 15 Mar 2025
Externally published	Yes

Keywords

Dirichlet heat kernel
Recilinear fractional Laplace operator
Rectilinear stable process
Transition density function

Access to Document

10.1016/j.jfa.2024.110812

Cite this

@article{f05f2a3af1644da093039b544e7bb9f9,

title = "Dirichlet heat kernel estimates for rectilinear stable processes",

abstract = "Let d≥2, α∈(0,2), and X be the rectilinear α-stable process on Rd. We first present a geometric characterization of open subset D⊂Rd so that the part process XD of X in D is irreducible. We then study the properties of the transition density functions of XD, including the strict positivity property as well as their sharp two-sided bounds in C1,1 domains in Rd. Our bounds are shown to be sharp for a class of C1,1 domains.",

keywords = "Dirichlet heat kernel, Recilinear fractional Laplace operator, Rectilinear stable process, Transition density function",

author = "Chen, {Zhen Qing} and Eryan Hu and Guohuan Zhao",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2025",

month = mar,

day = "15",

doi = "10.1016/j.jfa.2024.110812",

language = "English",

volume = "288",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "6",

}

TY - JOUR

T1 - Dirichlet heat kernel estimates for rectilinear stable processes

AU - Chen, Zhen Qing

AU - Hu, Eryan

AU - Zhao, Guohuan

PY - 2025/3/15

Y1 - 2025/3/15

N2 - Let d≥2, α∈(0,2), and X be the rectilinear α-stable process on Rd. We first present a geometric characterization of open subset D⊂Rd so that the part process XD of X in D is irreducible. We then study the properties of the transition density functions of XD, including the strict positivity property as well as their sharp two-sided bounds in C1,1 domains in Rd. Our bounds are shown to be sharp for a class of C1,1 domains.

AB - Let d≥2, α∈(0,2), and X be the rectilinear α-stable process on Rd. We first present a geometric characterization of open subset D⊂Rd so that the part process XD of X in D is irreducible. We then study the properties of the transition density functions of XD, including the strict positivity property as well as their sharp two-sided bounds in C1,1 domains in Rd. Our bounds are shown to be sharp for a class of C1,1 domains.

KW - Dirichlet heat kernel

KW - Recilinear fractional Laplace operator

KW - Rectilinear stable process

KW - Transition density function

UR - http://www.scopus.com/inward/record.url?scp=85214703309&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2024.110812

DO - 10.1016/j.jfa.2024.110812

M3 - Article

AN - SCOPUS:85214703309

SN - 0022-1236

VL - 288

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

M1 - 110812

ER -

Dirichlet heat kernel estimates for rectilinear stable processes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this