Sobolev spaces and Poincare inequalities on the Vicsek fractal

被引：8

作者：

Baudoin, Fabrice ^{[1
]}

Chen, Li ^{[2
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

ANNALES FENNICI MATHEMATICI | 2023年 / 48卷 / 01期

关键词：

Vicsek set; Sobolev spaces; Poincar? inequalities; p-energies; real interpolation; TRIEBEL-LIZORKIN SPACES; P-ENERGY; BESOV;

D O I：

10.54330/afm.122168

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove that several natural approaches to Sobolev spaces coincide on the Vicsek fractal. More precisely, we show that the metric approach of Korevaar-Schoen, the approach by limit of discrete p-energies and the approach by limit of Sobolev spaces on cable systems all yield the same functional space with equivalent norms for p > 1. As a consequence we prove that the Sobolev spaces form a real interpolation scale. We also obtain LP-Poincare inequalities for all values of p >= 1.

引用

页码：3 / 26

页数：24

共 27 条

[1] Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates [J].