Denk, Robert

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Some new thoughts on old results of R. T. Seeley

2004, Denk, Robert, Dore, Giovanni, Hieber, Matthias, Prüss, Jan, Venni, Alberto

In this paper we show that the Lp-reslization of a vector-valued elliptic boundary value problem (A,Bj) admits a bounded H-infinity calculus on Lp (G;E), p>1, provided the top-order coefficients of A are Hölder continuous. Here G denotes a domain in Rn 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-infinity calculus and kernel estimates for the solution of (A,Bj).