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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 712051, 11 pages
Research Article

Criterion on -Boundedness for Oscillatory Bilinear Hilbert Transform

School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing 100049, China

Received 18 November 2013; Accepted 28 December 2013; Published 25 February 2014

Academic Editor: Dashan Fan

Copyright © 2014 Zuoshunhua Shi and Dunyan Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the bilinear Hilbert transform with oscillatory factors and the truncated bilinear Hilbert transform. The main result is that the -boundedness of the two operators is equivalent with , and . In addition, we also discuss the boundedness of a variant operator of bilinear Hilbert transform with a nontrivial polynomial phase.