Linear operators, Fourier integral operators and \(k\)-plane transforms on rearrangement-invariant quasi-Banach function spaces
type: Item
instance of: scholarly article
title: Linear operators, Fourier integral operators and \(k\)-plane transforms on rearrangement-invariant quasi-Banach function spaces
zbMATH Open document ID: 1486.47061
author: Kwok-Pun Ho
published in: Positivity
publication date: 2021-05-07T00:00:00Z
review text: The main result of this paper concerns the mapping properties of linear operators on rearrangement-invariant quasi-Banach function spaces. It extends Boyd's interpolation theorem to the case where the linear operator \(T: L^p\rightarrow L^q\) is bounded with \(p\not= q\). The author establishes the mapping properties of the linear operator $T$ on rearrangement-invariant quasi-Banach function spaces, where \(T: L^p\rightarrow L^q\) is bounded with \(ap^{-1}=bq^{-1}+c\) for some \(a, b > 0\) and \(c\in\mathbb R\). The interpolation method given in [\textit{K.-P. Ho}, Ann. Acad. Sci. Fenn., Math. 41, No. 2, 897--922 (2016; Zbl 1355.42020)] is used. As applications of the main result, the mapping properties of Fourier integral operators, $k$-plane transforms and Radon transforms on rearrangement-invariant quasi-Banach function spaces are obtained.
reviewed by: Vadim D. Kryakvin
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 35S30
Mathematics Subject Classification ID: 44A05
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 7345604
zbMATH Keywords: mapping properties
zbMATH Keywords: interpolation
zbMATH Keywords: Fourier integral operators
zbMATH Keywords: Radon transform
zbMATH Keywords: X-ray transform
zbMATH Keywords: rearrangement-invariant quasi-Banach function spaces
MaRDI profile type: Publication
full work available at URL: s11117-020-00750-0
OpenAlex ID: W3014900526
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DOI: 10.1007/S11117-020-00750-0
description: scientific article; zbMATH DE number 7345604