On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains |
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Authors: | Rychkov Vyacheslav S. |
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Affiliation: | Mathematisches Institut, Friedrich-Schiller-Universität Jena Ernst-Abbe-Platz 14, 07743 Jena, Germany |
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Abstract: | The restrictions Bspq() and Fspq() of the Besov and TriebelLizorkinspaces of tempered distributions Bspq(Rn) and Fspq(Rn) to Lipschitzdomains Rn are studied. For general values of parameters (sR,p>0, q>0) a universal linear bounded extensionoperator from Bspq() and Fspq() into the corresponding spaceson Rn is constructed. The construction is based on a new variantof the Calderón reproducing formula with kernels supportedin a fixed cone. Explicit characterizations of the elementsof Bspq() and Fspq() in terms of their values in are also obtained. |
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