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.
"Criterion on -Boundedness for Oscillatory Bilinear Hilbert Transform." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/712051