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FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES

Part of: Approximations and expansions Linear function spaces and their duals Normed linear spaces and Banach spaces; Banach lattices Special classes of linear operators Harmonic analysis in one variable Integral transforms, operational calculus

Published online by Cambridge University Press:  20 June 2018

KWOK-PUN HO
KWOK-PUN HO*
Affiliation:
Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China e-mail: vkpho@eduhk.hk
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Abstract

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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.

MSC classification

Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 47B38: Operators on function spaces (general) 44A05: General transforms 46B70: Interpolation between normed linear spaces 41A05: Interpolation 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 231 - 248
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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