The ℓ s-boundedness of a family of integral operators on UMD banach function spaces
Emiel Lorist (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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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.