Operator-valued dyadic harmonic analysis beyond doubling measures
classification
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math.FAmath.OA
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borelhaarmeasuresoperator-valuedadaptedanalysisarbitrarybeyond
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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.
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