Bilinear Fractional Integral Along Homogeneous Curves

The boundedness of the bilinear fractional integrals along homogeneous curves \(\gamma (t)=(t^{\alpha _1},t^{\alpha _2})\) with \(\alpha _2>\alpha _1\ge 1\) is obtained. The authors extend the results of the bilinear fractional integrals of Kenig and Stein (Math Res Lett 6:1–15, 1999) and Grafakos and Kalton (Math Ann 319(1):151–180, 2001) to integrals along the curves.