Heat kernel gradient estimates for the Vicsek set

被引：0

作者：

Baudoin, Fabrice ^{[1
]}

Chen, Li ^{[2
]}

机构：

[1] Aarhus Univ, Dept Math, Aarhus, Denmark

[2] Louisiana State Univ, Dept Math, Los Angeles, CA USA

来源：

MATHEMATISCHE NACHRICHTEN | 2024年

基金：

美国国家科学基金会;

关键词：

heat kernel gradient bound; Vicsek set; BROWNIAN-MOTION; RIESZ TRANSFORM; SOBOLEV; INEQUALITIES; DERIVATIONS; POINCARE;

D O I：

10.1002/mana.202400180

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove pointwise and Lp$L<^>p$ gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its kernel.

引用

页数：28

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