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.
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Acknowledgments
We would like to express our sincere gratitude to the anonymous reviewer for his/her valuable advice and helpful comments on the earlier manuscript. This work was partially supported by NSF of China (Grant No. 11171026), the Fundamental Research Funds for the Central Universities (No. 2014KJJCA10) and Beijing Higher Education Young Elite Teacher Project.
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Communicated by Fulvio Ricci.
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Li, J., Liu, P. Bilinear Fractional Integral Along Homogeneous Curves. J Fourier Anal Appl 23, 1465–1479 (2017). https://doi.org/10.1007/s00041-016-9511-9
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DOI: https://doi.org/10.1007/s00041-016-9511-9