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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