@inbook{5f75055fa697497eb9a1e40382268f96,

title = "The ℓ s-boundedness of a family of integral operators on UMD banach function spaces",

abstract = "We prove the ℓs-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 ℓs-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of ℓs-boundedness as weighted boundedness by Rubio de Francia.",

keywords = "Banach function space, Hardy–Littlewood maximal operator, Integral operator, Muckenhoupt weights, UMD, ℓ-boundedness",

author = "Emiel Lorist",

year = "2019",

doi = "10.1007/978-3-030-10850-2_20",

language = "English",

isbn = "978-3-030-10849-6",

series = "Trends in Mathematics",

publisher = "Birkh{\"a}user",

pages = "365--379",

editor = "G. Buskes and {de Jeu}, M. and P. Dodds and A. Schep and F. Sukochev and {van Neerven}, J.",

booktitle = "Positivity and Noncommutative Analysis",

}