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

Abstract

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