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

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 not equal 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.