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 $B{\mathcal{I}}_{\hat{I}}\pm$ defined by \[ B\mathcal{I}_α({f,g})(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-α}}dy, \] with $0<\hat{I}\pm <n$. We prove the weighted boundedness of $B{\mathcal{I}}_{\hat{I}}\pm$ on the Morrey type spaces. Moreover, an Olsen type inequality for $B{\mathcal{I}}_{\hat{I}}\pm$ is also given.

25 pages