Fourier-type transforms on rearrangement-invariant quasi-Banach function spaces

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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.
LanguageEnglish
Pages231-248
JournalGlasgow Mathematical Journal
Volume61
Issue number1
Early online date20 Jun 2018
DOIs
Publication statusPublished - Jan 2019

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Quasi-Banach Space
Banach Function Space
Rearrangement
Transform
Invariant
Kontorovich-Lebedev Transform
Oscillatory Integrals
Hankel transform
Lebesgue Space
Integral Operator
Laplace transform
Functor
Interpolate

Citation

Ho, K.-P. (2019). Fourier-type transforms on rearrangement-invariant quasi-Banach function spaces. Glasgow Mathematical Journal, 61(1), 231-248. doi: 10.1017/S0017089518000186