Approximation and extension of functions of vanishing mean oscillation

DOI10.1007/s12220-020-00526-8zbMath1471.42049OpenAlexW3091790157MaRDI QIDQ2050527

Almaz Butaev, Galia Dafni

Publication date: 31 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-020-00526-8

zbMATH Keywords

extension theoremsvanishing mean oscillationuniform domainsbounded mean oscillationcontinuous mean oscillation

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (4)

Extension domains for Hardy spaces ⋮ \(C^\ast\)-algebras of poly-Bergman type operators with piecewise slowly oscillating coefficients ⋮ Locally uniform domains and extension of bmo functions ⋮ Vanishing mean oscillation and continuity of rearrangements

Cites Work

• Whitney's extension problem for \(C^m\)
• Uniform domains and the quasi-hyperbolic metric
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• On the compactness of operators of Hankel type
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• The BMO-Dirichlet problem for elliptic systems in the upper half-space and quantitative characterizations of VMO
• Degree theory of BMO. I: Compact manifolds without boundaries
• Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu)
• A sharp form of Whitney's extension theorem
• Lipschitz-type functions on metric spaces
• \(C^m\) extension by linear operators
• On functions of integrable mean oscillation
• Traces of $C^{k}$ functions on weak Markov subsets of $\mathbb R^{n}$
• On functions of bounded mean oscillation
• 𝐁𝐌𝐎 on shapes and sharp constants
• Functions of Vanishing Mean Oscillation
• Some properties of functions with bounded mean oscillation
• Extensions of Hardy spaces and their use in analysis
• Rings of functions in Lipschitz topology
• Sobolev Spaces on Metric Measure Spaces
• Mean Oscillation Over Cubes and Holder Continuity
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