Linear operators, Fourier integral operators and \(k\)-plane transforms on rearrangement-invariant quasi-Banach function spaces
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.
rearrangement-invariant quasi-Banach function spaces
scientific article; zbMATH DE number 7345604
scientific article