Mapping properties for the homogeneous fractional integral operator $T_{{\mit \Omega},\alpha}$ on the Hardy spaces $H^p(R^n)$ are studied. Our results give the extension of Stein-Weiss and Taibleson-Weiss's results for the boundedness of the Riesz potential operator $I_{\alpha}$ on the Hardy spaces $H^p(R^n)$.
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