Some estimates for the bilinear fractional integrals on the Morrey space (1808.05189v1)

Abstract: In this paper, we are interested in the following bilinear fractional integral operator $B\mathcal{I}\alpha$ defined by [ B\mathcal{I}{\alpha}({f,g})(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-\alpha}}dy, ] with $0< \alpha<n$. We prove the weighted boundedness of $B\mathcal{I}\alpha$ on the Morrey type spaces. Moreover, an Olsen type inequality for $B\mathcal{I}\alpha$ is also given.