New thoughts on old results of R. T. Seeley
R. Denk, G. Dore, M. Hieber, J. Prüss, and A. Venni
Abstract. In this paper we show that the Lp-realization 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).
Math. Ann. 328 (2004), 545-583.
The paper is available here: pdf