Title: Rescaled extrapolation for vector-valued functions,
Abstract: We extend Rubio de Francia's extrapolation theorem for functions valued in
UMD Banach function spaces, leading to short proofs of some new and known
results. In particular we prove Littlewood-Paley-Rubio de Francia-type
estimates and boundedness of variational Carleson operators for Banach function
spaces with UMD concavifications.