Geodesic
FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES
Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 231-248

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DOI

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. 
HO, KWOK-PUN. FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES. Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 231-248. doi: 10.1017/S0017089518000186
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     author = {HO, KWOK-PUN},
     title = {FOURIER-TYPE {TRANSFORMS} {ON} {REARRANGEMENT-INVARIANT} {QUASI-BANACH} {FUNCTION} {SPACES}},
     journal = {Glasgow mathematical journal},
     pages = {231--248},
     year = {2019},
     volume = {61},
     number = {1},
     doi = {10.1017/S0017089518000186},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000186/}
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