This is an announcement for the paper “The $\ell^s$-boundedness of a family of integral operators on UMD Banach function spaces” by Emiel Loristhttps://arxiv.org/search/math?searchtype=author&query=Lorist%2C+E.

Abstract: We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1810.12833