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New thoughts on old results of R.T. Seeley

Author： Denk Robert

Publisher： Springer Publishing Company

ISSN： 0025-5831

Source： Mathematische Annalen, Vol.328, Iss.4, 2004-04, pp. : 545-583

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

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

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