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ON RESTRICTIONS AND EXTENSIONS OF THE BESOV AND TRIEBEL–LIZORKIN SPACES WITH RESPECT TO LIPSCHITZ DOMAINS

Published online by Cambridge University Press:  01 August 1999

VYACHESLAV S. RYCHKOV
VYACHESLAV S. RYCHKOV
Affiliation:
Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 1–4, 07743 Jena, Germany Current address: Mathematics Department, Princeton University, Princeton, NJ 08544, USA; rytchkov@math.princeton.edu
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Abstract

The restrictions Bspq(Ω) and Fspq(Ω) of the Besov and Triebel–Lizorkin spaces of tempered distributions Bspq(ℝn) and Fspq(ℝn) to Lipschitz domains Ω⊂ℝn are studied. For general values of parameters (s∈ℝ, p>0, q>0) a ‘universal’ linear bounded extension operator from Bspq(Ω) and Fspq(Ω) into the corresponding spaces on ℝn is constructed. The construction is based on a new variant of the Calderón reproducing formula with kernels supported in a fixed cone. Explicit characterizations of the elements of Bspq(Ω) and Fspq(Ω) in terms of their values in Ω are also obtained.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 237 - 257
Copyright
The London Mathematical Society 1999

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Footnotes

This work was supported by the Russian Foundation for Basic Research, pr. 96-01-00243.