Pettis integrals with singular kernels (Q1086791)

Singular integral operators typically arise from the solution of partial differential equations on \(L^ p\)-spaces of functions on \({\mathbb{R}}^ d\). The purpose of this article is to show that the singular integral operators coming from the construction of resolvent operators for elliptic partial differential equations on Euclidean space can be represented as proper operator valued integrals - the Pettis integral of operator valued functions. The representation is used to develop a functional calculus in a companion paper, ibid. 635-653 (1986; review below).