New thoughts on old results of R.T. Seeley

Robert Denk; Giovanni Dore; Matthias Georg Hieber; Jan Prüss; Alberto Venni

New thoughts on old results of R.T. Seeley

Robert Denk^*, Giovanni Dore, Matthias Georg Hieber, Jan Prüss, Alberto Venni

^*この研究の対応する著者

研究成果: Article › 査読

78 被引用数 (Scopus)

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In this paper we show that the L_p -realization of a vector-valued elliptic boundary value problem (A, B_j) admits a bounded H^∞-calculus on L_P(G; E), 1 <p <∞, provided the top-order coefficients of A are Hölder continuous. Here G denotes a domain in ℝⁿ with compact C^2m- boundary and E a Banach space of class HT. Our proof is based on an abstract perturbation result for operators admitting bounded H^∞-calculus and kernel estimates for the solution of (A, B_j).

本文言語	English
ページ（範囲）	545-583
ページ数	39
ジャーナル	Mathematische Annalen
巻	328
号	4
出版ステータス	Published - 2004 4月
外部発表	はい

ASJC Scopus subject areas

数学 (全般)

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引用スタイル

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abstract = "In this paper we show that the Lp -realization of a vector-valued elliptic boundary value problem (A, Bj) admits a bounded H∞-calculus on LP(G; E), 1 n with compact C2m- boundary and E a Banach space of class HT. Our proof is based on an abstract perturbation result for operators admitting bounded H∞-calculus and kernel estimates for the solution of (A, Bj).",

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N2 - In this paper we show that the Lp -realization of a vector-valued elliptic boundary value problem (A, Bj) admits a bounded H∞-calculus on LP(G; E), 1 n with compact C2m- boundary and E a Banach space of class HT. Our proof is based on an abstract perturbation result for operators admitting bounded H∞-calculus and kernel estimates for the solution of (A, Bj).

AB - In this paper we show that the Lp -realization of a vector-valued elliptic boundary value problem (A, Bj) admits a bounded H∞-calculus on LP(G; E), 1 n with compact C2m- boundary and E a Banach space of class HT. Our proof is based on an abstract perturbation result for operators admitting bounded H∞-calculus and kernel estimates for the solution of (A, Bj).

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New thoughts on old results of R.T. Seeley

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