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The s-Boundedness of a Family of Integral Operators on UMD Banach Function Spaces

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Positivity and Noncommutative Analysis

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Abstract

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

Dedicated to Ben de Pagter on the occasion of his 65th birthday

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Acknowledgements

The author would like to thank Mark Veraar and Jan van Neerven for carefully reading the draft version of this paper. Author Emiel Lorist is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).

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Lorist, E. (2019). The s-Boundedness of a Family of Integral Operators on UMD Banach Function Spaces. In: Buskes, G., et al. Positivity and Noncommutative Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-10850-2_20

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