A pointwise estimate for positive dyadic shifts and some applications
  We prove a pointwise estimate for positive dyadic shifts of complexity $m$ which is linear in the complexity. This can be used to give a pointwise estimate for Calder\'on-Zygmund operators and to answer a question posed by A. Lerner. Several applications to weighted estimates for both multilinear Calder\'on-Zygmund operators and square functions are discussed. 
Jose M. Conde-Alonso and Guillermo Rey
math.CA