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This paper mainly dedicates to prove a plethora of weighted estimates onMorrey spaces for bilinear fractional integral operators and their generalcommutators with BMO functions of the form$$B_{\alpha}(f,g)(x)=\int_{\mathbb{R}^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-\alpha}}dy,\qquad0<\alpha<n.$$ We also prove some maximal function control theorems for theseoperators, that is, the weighted Morrey norm is bounded by the weighted Morreynorm of a natural maximal operator when the weight belongs to $A_{\infty}$. Asa corollary, some new weighted estimates for the bilinear maximal functionassociated to the bilinear Hilbert transform are obtained. Furthermore, weformulate a bilinear version of Stein-Weiss inequality on Morrey spaces forfractional integrals.

Weighted estimates for bilinear fractional integral operators and their commutators on Morrey spaces