Some estimates for the bilinear fractional integrals on the Morrey space

Abstract

In this paper, we are interested in the following bilinear fractional integral operator BI α defined by BI α (f ,g)(x) = R n f (x − y)g(x + y) |y| n−α dy, with 0 < α < n. We prove the weighted boundedness of BI α on the Morrey type spaces. Moreover, an Olsen type inequality for BI α is also given.