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 arbi...
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| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.1412.4937 |