Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems
Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems
Muscalu, Pipher, Tao and Thiele \cite{MPTT} showed that the tensor product between two one dimensional paraproducts (also known as bi-parameter paraproduct) satisfies all the expected $L^p$ bounds. In the same paper they showed that the tensor product between two bilinear Hilbert transforms is unbounded in any range. They also raised …