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.
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页数：28
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