Optimality of function spaces for kernel integral operators

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.