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

Glasgow Mathematical Journal ◽

10.1017/s0017089518000186 ◽

2018 ◽

Vol 61 (1) ◽

pp. 231-248 ◽

Cited By ~ 6

Author(s):

KWOK-PUN HO

Keyword(s):

Banach Function Space ◽

Integral Operators ◽

Oscillatory Integral ◽

Function Spaces ◽

Lebesgue Spaces ◽

Banach Function Spaces ◽

Oscillatory Integral Operators ◽

Interpolation Functor ◽

The Laplace Transform ◽

Fourier Type

AbstractWe 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.

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