Abstract
We establish the mapping properties of Fourier-type transforms on rearrangement-invariant quasi-Banach function spaces. In particular, we have the mapping properties of the Laplace transform, the Hankel transforms, the Kontorovich-Lebedev transform and some oscillatory integral operators. We achieve these mapping properties by using an interpolation functor that can explicitly generate a given rearrangement-invariant quasi-Banach function space via Lebesgue spaces. Copyright © 2018 Glasgow Mathematical Journal Trust.
| Original language | English |
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| Pages (from-to) | 231-248 |
| Journal | Glasgow Mathematical Journal |
| Volume | 61 |
| Issue number | 1 |
| Early online date | 20 Jun 2018 |
| DOIs | |
| Publication status | Published - Jan 2019 |