The dichotomy between traces on \(d\)-sets \(\Gamma \) in \(\mathbb R^n\) and the density of \(D(\mathbb R^n \setminus \Gamma )\) in function spaces

DOI10.1007/s10114-007-7007-xzbMath1161.46021OpenAlexW2106822002MaRDI QIDQ943495

Hans Triebel

Publication date: 9 September 2008

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-007-7007-x

zbMATH Keywords

fractalstracesfunction spaces\(d\)-sets

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractals (28A80)

Related Items (8)

Traces of Besov and Triebel‐Lizorkin spaces on domains ⋮ Spectral theory for perturbed Krein Laplacians in nonsmooth domains ⋮ Dichotomy in Muckenhoupt Weighted Function Space: A Fractal Example ⋮ On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space ⋮ Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces ⋮ Sobolev spaces on non-Lipschitz subsets of \(\mathbb {R}^n\) with application to boundary integral equations on fractal screens ⋮ A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains ⋮ Density results for Sobolev, Besov and Triebel-Lizorkin spaces on rough sets

Cites Work

• A discrete transform and decompositions of distribution spaces
• Sets of singularities of functions in spaces of Besov and Lizorkin- Triebel type
• Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains
• Tailored Besov spaces andh-sets
• Atomic Decompositions of F Spaces. Applications to Exotic Pseudodifferential and Fourier Integral Operators
• A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces
• An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation
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