A bounded linear extension operator for \(L^{2,p}(\mathbb R^2)\)

DOI10.4007/annals.2013.178.1.3zbMath1315.46034arXiv1011.0689OpenAlexW2963754828MaRDI QIDQ355135

Arie Israel

Publication date: 24 July 2013

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0689

zbMATH Keywords

interpolationSobolev spacesextensionWhitney extension problemlinear extension operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and differentiation questions (26B05)

Related Items (10)

Smooth convex extensions of convex functions ⋮ On planar Sobolev \(L_p^m\)-extension domains ⋮ Linear extension operators for Sobolev spaces on radially symmetric binary trees ⋮ Approximate extension in Sobolev space ⋮ Sobolev -spaces on -thick closed subsets of ⋮ Nonnegative \(\mathrm C^2(\mathbb R^2)\) interpolation ⋮ Extension criteria for homogeneous Sobolev spaces of functions of one variable ⋮ The structure of Sobolev extension operators ⋮ \(C^{1, \omega }\) extension formulas for $1$-jets on Hilbert spaces ⋮ Sobolev extension by linear operators

Cites Work

• The structure of Sobolev extension operators
• Whitney's extension problem for \(C^m\)
• \(C^{m,\omega}\) extension by bounded-depth linear operators
• Sobolev \(W_p^1\)-spaces on closed subsets of \(\mathbf R^n\)
• Extension of \(C^{m, \omega}\)-smooth functions by linear operators
• Traces of functions of Zygmund class
• The Whitney problem of existence of a linear extension operator
• A sharp form of Whitney's extension theorem
• Fitting a \(C^m\)-smooth function to data. I.
• \(C^m\) extension by linear operators
• Interpolation and extrapolation of smooth functions by linear operators
• Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions
• Sobolev extension by linear operators
• Book Review: Methods of geometric analysis in extension and trace problems. Volume 1; Methods of geometric analysis in extension and trace problems. Volume 2
• Analytic Extensions of Differentiable Functions Defined in Closed Sets
• Differentiable Functions Defined in Closed Sets. I
• The characterization of functions arising as potentials
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