The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 224–246 | Cite as

Quasi Pieces of the Bilinear Hilbert Transform Incorporated into a Paraproduct

  • Dong Dong


We prove the boundedness of a class of tri-linear operators consisting of a quasi piece of bilinear Hilbert transform whose scale equals to or dominates the scale of its linear counter part. Such type of operators is motivated by the tri-linear Hilbert transform and its curved versions.


Bilinear Hilbert transform Paraproduct Tri-linear operators 

Mathematics Subject Classification

42A50 47G10 42B99 



The author would like to thank Prof. Xiaochun Li for helpful discussions on this topic. He also acknowledges the support from Gene H. Golub Fund of Mathematics Department at University of Illinois.


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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