\(p\)-Poincaré inequality versus \(\infty \)-Poincaré inequality: some counterexamples

DOI10.1007/S00209-011-0871-1zbMath1255.46015OpenAlexW2044004866WikidataQ109994480 ScholiaQ109994480MaRDI QIDQ431297

Alex Williams, Nageswari Shanmugalingam, Estibalitz Durand-Cartagena

Publication date: 26 June 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-011-0871-1

zbMATH Keywords

Poincaré inequalities\({{\mathcal{A}}_{\infty}}\) weights\(p\)-thick convexitydoubling metric measure spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Axiomatic and generalized convexity (52A01) Fractals (28A80) Potential theory on fractals and metric spaces (31E05) Quasiconformal mappings in metric spaces (30L10)

Related Items (6)

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality ⋮ Infinity modulus and the essential metric ⋮ Prime ends for domains in metric spaces ⋮ Existence and uniqueness of \(\infty \)-harmonic functions under assumption of \(\infty \)-Poincaré inequality ⋮ Maximal metric surfaces and the Sobolev-to-Lipschitz property ⋮ Gradient estimates for heat kernels and harmonic functions

Cites Work

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• Nonlinear potential theory on metric spaces
• The boundary correspondence under quasiconformal mappings
• Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
• Pointwise Lipschitz functions on metric spaces
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Modulus and the Poincaré inequality on metric measure spaces
• Lectures on analysis on metric spaces
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
• The \(\infty \)-Poincaré inequality on metric measure spaces
• The Poincaré inequality is an open ended condition
• Geometric implications of the Poincaré inequality
• Lectures on \(n\)-dimensional quasiconformal mappings
• Sobolev met Poincaré
• Admissible measures in one dimension

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