Linear operators, Fourier integral operators and k-plane transforms on rearrangement-invariant quasi-Banach function spaces

Kwok Pun Victor HO

doi:10.1007/s11117-020-00750-0

Linear operators, Fourier integral operators and k-plane transforms on rearrangement-invariant quasi-Banach function spaces

Kwok Pun Victor HO

Department of Mathematics and Information Technology (MIT)

Research output: Contribution to journal › Articles › peer-review

17 Citations (Scopus)

Abstract

We establish the mapping properties of linear operators on rearrangement-invariant quasi-Banach function spaces. Our result applies to those linear operators that map L^p to L^q with p ≠ q. Therefore, it can be used to study the mapping properties of the fractional integral operators, the Fourier integral operators and the k-plane transforms on rearrangement-invariant quasi-Banach function spaces. Copyright © 2020 Springer Nature Switzerland AG.

Original language	English
Pages (from-to)	73-96
Journal	Positivity
Volume	25
Issue number	1
Early online date	03 Apr 2020
DOIs	https://doi.org/10.1007/s11117-020-00750-0
Publication status	Published - Feb 2021

Keywords

Linear operator
Interpolation
Fourier integral operators
Radon transform
X-ray transform
Rearrangement-invariant quasi-Banach function spaces

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10.1007/s11117-020-00750-0

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AB - We establish the mapping properties of linear operators on rearrangement-invariant quasi-Banach function spaces. Our result applies to those linear operators that map Lp to Lq with p ≠ q. Therefore, it can be used to study the mapping properties of the fractional integral operators, the Fourier integral operators and the k-plane transforms on rearrangement-invariant quasi-Banach function spaces. Copyright © 2020 Springer Nature Switzerland AG.

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Linear operators, Fourier integral operators and k-plane transforms on rearrangement-invariant quasi-Banach function spaces

Abstract

Keywords

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