Optimality of function spaces for kernel integral operators |
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| Authors: | Jakub Takáč |
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| Institution: | Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Czech Republic |
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| 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. |
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| Keywords: | kernel integral operator Lorentz space Marcinkiewicz space optimal range Peetre K-functional rearrangement-invariant space |
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