# Bilinear Fractional Integral Along Homogeneous Curves

Research paper by **Junfeng Li, Peng Liu**

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

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#### 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