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.
Alex Amenta. Emiel Lorist. Mark Veraar. "Rescaled extrapolation for vector-valued functions." Publ. Mat. 63 (1) 155 - 182, 2019. https://doi.org/10.5565/PUBLMAT6311905