Dunyan Yan 

"Singular Integral Transform of Product  Functions"

Abstract:
 We first give a necessary and sufficient condition which ensures
 validity of the Bedrosian identity of the Hilbert transform of
 product functions $fg$. Convenient sufficient conditions are
 presented, which cover the classical Bedrosian theorem. Then we
 extend the Bedrosian identity for the Hilbert transform of product
 functions  to Calder\'on-Zygmund singular integral transform. A
 counterexample shows that sufficient conditions on one-dimensional
 Euclidean space does not ensure the validity of  the Bedrosian
 identity for n-dimensional case. In final, we construct some
 approximation theorems on product function in  replacing identity of
 Bedrosian Theorem.