Operator-valued dyadic harmonic analysis beyond doubling measures
  We obtain a complete characterization of the weak-type $(1,1)$ for Haar shift operators in terms of generalized Haar systems adapted to a Borel measure $\mu$ in the operator-valued setting. The main technical tool in our method is a noncommutative Calder\'on-Zygmund decomposition valid for arbitrary Borel measures. 
Jos\'e M. Conde-Alonso, Luis Daniel L\'opez-S\'anchez
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