Abstract
We study the quasi-extremizers of a specified linear operator T:Lp →Lq in order to find an extremizer. This operator is a basic example of the generalized Radon transforms. We first includes some properties of paraballs for a better situation of approximation. Then these properties help us to deal with different type of quasi-extremizers. Finally, a good quasiextremizing sequence appraoches to an extremizer, by its inner product form.