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The dichotomy between traces on d-sets Γ in ℝn and the density of D(ℝn\Γ) in function spaces

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Abstract

A space A s pq (ℝn) with A = B or A = F and s ∈ ℝ, 0 < p,q < ∞ either has a trace in L p (Γ), where Γ is a compact d-set in ℝn with 0 < d < n, or D(ℝnΓ) is dense in it. Related dichotomy numbers are introduced and calculated.

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  1. Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07737, Jena, Germany

    Hans Triebel

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  1. Hans Triebel
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Triebel, H. The dichotomy between traces on d-sets Γ in ℝn and the density of D(ℝn\Γ) in function spaces. Acta. Math. Sin.-English Ser. 24, 539–554 (2008). https://doi.org/10.1007/s10114-007-7007-x

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  • DOI: https://doi.org/10.1007/s10114-007-7007-x

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