Bilinear Fractional Integral Along Homogeneous Curves

Abstract 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) an...
Ausführliche Beschreibung

Abstract 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. Ausführliche Beschreibung