Weighted Weak (1,1) estimates for one-sided oscillatory singular   integrals
  We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities of a class of one-sided oscillatory singular integrals with smooth kernel. 
Zunwei Fu, Shanzhen Lu, Shuichi Sato and Shaoguang Shi
math.FA