We prove a (sharp) 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 Calderón-Zygmund operators and to answer a question originally posed by Lerner. Several applications to weighted estimates for both multilinear Calderón-Zygmund operators and square functions are discussed.
Bibliographical noteFunding Information:
J. M. Conde-Alonso was partially supported by the ERC StG-256997-CZOSQP, the Spanish Grant MTM2010-16518 and by ICMAT Severo Ochoa Grant SEV-2011-0087 (Spain).
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