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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

80 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	545-583
Number of pages	39
Journal	Mathematische Annalen
Volume	328
Issue number	4
Publication status	Published - 2004 Apr
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "New thoughts on old results of R.T. Seeley",

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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AU - Dore, Giovanni

AU - Hieber, Matthias Georg

AU - Prüss, Jan

AU - Venni, Alberto

PY - 2004/4

Y1 - 2004/4

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

Abstract

ASJC Scopus subject areas

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