Boundedness of fractional integral operators with rough kernels on weighted Morrey spaces

Let $M_{\mathrm{\Omega },\alpha }$ and $T_{\mathrm{\Omega },\alpha }$ be the fractional maximal and integral operators with rough kernels, where $0<\alpha <n$. In this paper, we shall study the continuity properties of $M_{\mathrm{\Omega },\alpha }$ and $T_{\mathrm{\Omega },\alpha }$ on the weighted Morrey spaces $L^{p,\kappa }(w)$. The boundedness of their commutators with BMO functions is also obtained.