## Tohoku Mathematical Journal 2000 March SECOND SERIES VOL. 52, NO. 1

 Tohoku Math. J. 52 (2000), 153-162

Title HOMOGENEOUS FRACTIONAL INTEGRALS ON HARDY SPACES

Author Yong Ding and Shanzhen Lu

(Received September 18, 1998, revised April 22, 1999)
Abstract. Mapping properties for the homogeneous fractional integral operator $T_{{\mit \Omega},\alpha}$ on the Hardy spaces $H^p(\boldsymbol{R}^n)$ 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 $H^p(\boldsymbol{R}^n)$.

1991 Mathematics Subject Classification. Primary 42B25.

Key words and phrases. Fractional integral, homogeneous kernel, $L^r$-Dini condition, $H^p$ space.

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