Sobolev spaces and Poincaré inequalities on the Vicsek fractal
type: Item
instance of: scholarly article
title: Sobolev spaces and Poincaré inequalities on the Vicsek fractal
author: Fabrice Baudoin
author: Li Chen
published in: Annales Fennici Mathematici
publication date: 2022-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/2207.02949
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46B70
zbMATH DE Number: 7608235
zbMATH Keywords: vicsek set
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Poincaré inequalities
zbMATH Keywords: p-energies
zbMATH Keywords: real interpolation
MaRDI profile type: Publication
OpenAlex ID: W4303621867
cites work: Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces
cites work: Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities
cites work: Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates
cites work: Differential one-forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs
cites work: Q4039801
cites work: \(p\)-energies on p.c.f. self-similar sets
cites work: A note on Sobolev type inequalities on graphs with polynomial volume growth
cites work: Analysis of the Laplacian and spectral operators on the Vicsek set
cites work: Interpolation properties of Besov spaces defined on metric spaces
cites work: Q3062378
cites work: Heat kernel and Lipschitz-Besov spaces
cites work: Sobolev spaces on an arbitrary metric space
cites work: A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces
cites work: Quasiconformal maps in metric spaces with controlled geometry
cites work: Sobolev Spaces on Metric Measure Spaces
cites work: \(p\)-energy and \(p\)-harmonic functions on Sierpinski gasket type fractals
cites work: Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals
cites work: A note on Hajłasz-Sobolev spaces on fractals
cites work: Q4676348
cites work: Geometry and Analysis of Metric Spaces via Weighted Partitions
cites work: A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces
cites work: Heat kernel characterisation of Besov-Lipschitz spaces on metric measure spaces
cites work: Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals
cites work: Real interpolations for Besov and Triebel‐Lizorkin spaces on spaces of homogeneous type
DOI: 10.54330/AFM.122168
Recommended article: Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals
Recommended article: Sobolev Spaces and Calculus of Variations on Fractals
Recommended article: Fractional Poincaré and logarithmic Sobolev inequalities for measure spaces
Recommended article: Fractional Sobolev Spaces and Inequalities
Recommended article: A note on Hajłasz-Sobolev spaces on fractals
Recommended article: Poincaré inequalities and Sobolev spaces
Recommended article: Fractional Sobolev-Poincaré inequalities in irregular domains
Recommended article: Pointwise inequalities and approximation in fractional Sobolev spaces
Recommended article: Q4427641
Recommended article: Poincaré and Friedrichs inequalities in abstract Sobolev spaces
description: scientific article; zbMATH DE number 7608235