Extension of Pettis integration: Pettis operators and their integrals

In this note, the authors discuss the concepts of a Pettis operator , by which they mean a weak ∗ –weakly continuous linear operator F from a dual Banach space to an L 1 -space, and of its Pettis integral , understood simply as the dual operator F ∗ of F . Applications to radial limits in weak Hardy spaces of vector-valued harmonic and holomorphic functions are provided.