Operator-valued dyadic harmonic analysis beyond doubling measures

Operator-valued dyadic harmonic analysis beyond doubling measures

We obtain a complete characterization of the weak-type (1,1)(1,1) for Haar shift operators in terms of generalized Haar systems adapted to a Borel measure μ\mu in the operator-valued setting. The main technical tool in our method is a noncommutative Calderón-Zygmund decomposition valid for arbitrary...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2016-09, Vol.144 (9), p.3869-3885
Hauptverfasser: Conde-Alonso, José M., López-Sánchez, Luis Daniel
Format: Artikel
Sprache:eng
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B. ANALYSIS
Research article
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Zusammenfassung:We obtain a complete characterization of the weak-type (1,1)(1,1) for Haar shift operators in terms of generalized Haar systems adapted to a Borel measure μ\mu in the operator-valued setting. The main technical tool in our method is a noncommutative Calderón-Zygmund decomposition valid for arbitrary Borel measures.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13073