# Bilinear Fractional Integral Along Homogeneous Curves

Research paper by Junfeng Li, Peng Liu

Indexed on: 09 Nov '16Published on: 01 Nov '16Published in: Journal of Fourier Analysis and Applications

#### Abstract

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.AbstractThe 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. $$\gamma (t)=(t^{\alpha _1},t^{\alpha _2})$$ $$\gamma (t)=(t^{\alpha _1},t^{\alpha _2})$$ $$\alpha _2>\alpha _1\ge 1$$ $$\alpha _2>\alpha _1\ge 1$$19992001