Criterion on L p 1 × L p 2 → L q -Boundedness for Oscillatory Bilinear Hilbert Transform

الملخص EN

We investigate the bilinear Hilbert transform with oscillatory factors and the truncated bilinear Hilbert transform.

The main result is that the L p 1 × L p 2 → L q -boundedness of the two operators is equivalent with 1 ≤ p 1 , p 2 < ∞ , and 1 / 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.