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Optimality of function spaces for kernel integral operators

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  • Jakub Takáč

Abstract

We explore boundedness properties of kernel integral operators acting on rearrangement‐invariant (r.i.) spaces. In particular, for a given r.i. space X we characterize its optimal range partner, that is, the smallest r.i. space Y such that the operator is bounded from X to Y. We apply the general results to Lorentz spaces to illustrate their strength.

Suggested Citation

  • Jakub Takáč, 2023. "Optimality of function spaces for kernel integral operators," Mathematische Nachrichten, Wiley Blackwell, vol. 296(9), pages 4429-4453, September.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:9:p:4429-4453
    DOI: 10.1002/mana.201900545
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    References listed on IDEAS

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    1. Vít Musil & Rastislav Oľhava, 2019. "Interpolation theorem for Marcinkiewicz spaces with applications to Lorentz gamma spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 292(5), pages 1106-1121, May.
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