New thoughts on old results of R.T. Seeley

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 (infinity)-calculus on L-p(G;E), 1<p<infinity, provided the top-order coefficients of are Holder 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 (infinity)-calculus and kernel estimates for the solution of (A,B-j).