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

1 Citation (Scopus)

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

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10.1016/j.jfa.2024.110812

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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",

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AU - Chen, Zhen Qing

AU - Hu, Eryan

AU - Zhao, Guohuan

PY - 2025/3/15

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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 - https://www.scopus.com/pages/publications/85214703309

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

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Keywords

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