Criterion on Lp1×Lp2→Lq-Boundedness for Oscillatory Bilinear Hilbert Transform. (25th February 2014) - Shi, Zuoshunhua; Yan, Dunyan
Abstract : We investigate the bilinear Hilbert transform with oscillatory factors and the truncated bilinear Hilbert transform. The main result is that theL p 1 × L p 2 → L q -boundedness of the two operators is equivalent with1 ≤ p 1, p 2 < ∞, and1 / q = 1 / p 1 + 1 / p 2 . In addition, we also discuss the boundedness of a variant operator of bilinear Hilbert transform with a nontrivial polynomial phase.