Poincaré inequality meets Brezis-Van Schaftingen-Yung formula on metric measure spaces

DOI10.1016/j.jfa.2022.109645zbMath1504.46049arXiv2111.09755OpenAlexW3211643850MaRDI QIDQ2165546

Feng Dai, Yangyang Zhang, Xiaosheng Lin, Wen Yuan, Da Chun Yang

Publication date: 20 August 2022

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.09755

zbMATH Keywords

Poincaré inequalityfractional Sobolev inequalityGagliardo-Nirenberg inequalityBrezis-Van Schaftingen-Yung formula

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities in metric spaces (30L15) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Related Items (5)

Anisotropic versions of the Brezis-Van Schaftingen-Yung approach at \(s = 1\) and \(s = 0\) ⋮ Generalized Brezis-Seeger-Van Schaftingen-Yung formulae and their applications in ball Banach Sobolev spaces ⋮ Brezis-van Schaftingen-Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo-Nirenberg inequalities ⋮ Gagliardo representation of norms of ball quasi-Banach function spaces ⋮ The Bourgain-Brezis-Mironescu formula on ball Banach function spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Criterion of the boundedness of singular integrals on spaces of homogeneous type
• Hitchhiker's guide to the fractional Sobolev spaces
• Uniform estimates and limiting arguments for nonlocal minimal surfaces
• Gradient potential estimates
• Geometry and Hardy spaces on spaces of homogeneous type in the sense of Coifman and Weiss
• A new formula for the \(L^p\) norm
• A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa
• Lifting in Sobolev spaces
• Lectures on analysis on metric spaces
• Sobolev classes of Banach space-valued functions and quasiconformal mappings
• Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces on an arbitrary metric space
• Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail
• Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung
• Sobolev spaces revisited
• Sharp weighted estimates for square functions associated to operators on spaces of homogeneous type
• The Poincaré inequality is an open ended condition
• Polynomial approximation with doubling weights having finitely many zeros and singularities
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Bourgain-Brezis-Mironescu convergence via Triebel-Lizorkin spaces
• Singular integrals on Carleson measure spaces ${CMO}^p$ on product spaces of homogeneous type
• Introduction to Smooth Manifolds
• ATOMIC DECOMPOSITION OF WEIGHTED TRIEBEL–LIZORKIN SPACES ON SPACES OF HOMOGENEOUS TYPE
• The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
• Nonlocal minimal surfaces
• Extensions of Hardy spaces and their use in analysis
• Sobolev met Poincaré
• Maximal function characterizations for new local Hardy-type spaces on spaces of homogeneous type
• Classical Fourier Analysis
• Sobolev Spaces on Metric Measure Spaces
• Degenerate Poincaré–Sobolev inequalities
• Sobolev Spaces
• Best approximation and moduli of smoothness for doubling weights

This page was built for publication: Poincaré inequality meets Brezis-Van Schaftingen-Yung formula on metric measure spaces