On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains

Authors:	Rychkov Vyacheslav S

Institution:	Mathematisches Institut, Friedrich-Schiller-Universität Jena Ernst-Abbe-Platz 1–4, 07743 Jena, Germany

Abstract:	The restrictions B^s_pq( ${Omega}$ ) and F^s_pq( ${Omega}$ ) of the Besov and Triebel–Lizorkinspaces of tempered distributions B^s_pq(Rⁿ) and F^s_pq(Rⁿ) to Lipschitzdomains ${Omega}$ $sub$ Rⁿ are studied. For general values of parameters (s $isin$ R,p>0, q>0) a ‘universal’ linear bounded extensionoperator from B^s_pq( ${Omega}$ ) and F^s_pq( ${Omega}$ ) 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 B^s_pq( ${Omega}$ ) and F^s_pq( ${Omega}$ ) in terms of their values in ${Omega}$ are also obtained.

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