Optimality of function spaces for kernel integral operators

Jakub Takáč

Mathematische Nachrichten, 2023, vol. 296, issue 9, 4429-4453

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.

Date: 2023
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