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

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Positivity and Noncommutative Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

We prove the ℓ 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 ℓ s-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of ℓ 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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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Emiel Lorist

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  1. Emiel Lorist
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Correspondence to Emiel Lorist .

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Editors and Affiliations

  1. Department of Mathematics, University of Mississippi, Oxford, MS, USA

    Gerard Buskes

  2. Mathematical Institute, Leiden University, Leiden, The Netherlands; Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Marcel de Jeu

  3. College of Science and Engineering, Flinders University, Adelaide, Australia

    Peter Dodds

  4. Department of Mathematics, University of South Carolina, Columbia, SC, USA

    Anton Schep

  5. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Fedor Sukochev

  6. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Jan van Neerven

  7. Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast, UK

    Anthony Wickstead

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Lorist, E. (2019). The ℓ 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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