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We give a concise exposition of the basic theory of functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator $f(T₁,...,T_{N})$ when f is an R-bounded operator-valued holomorphic function.
In this paper we show that the Lp-realization of a vector-valued elliptic boundary value problem (, j) admits a bounded -calculus on Lp(G;E), 1p, provided the top-order coefficients of are Hlder continuous. Here G denotes a domain in n with compact C2m-boundary and E a Banach space of class . Our proof is based on an abstract perturbation result for operators admitting bounded -calculus and kernel...
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