Operator-valued dyadic harmonic analysis beyond doubling measures
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- by José M. Conde-Alonso and Luis Daniel López-Sánchez PDF
- Proc. Amer. Math. Soc. 144 (2016), 3869-3885 Request permission
Abstract:
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 Calderón-Zygmund decomposition valid for arbitrary Borel measures.References
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Additional Information
- José M. Conde-Alonso
- Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, E-28049 Madrid, Spain
- MR Author ID: 994319
- Email: jose.conde@icmat.es
- Luis Daniel López-Sánchez
- Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, E-28049 Madrid, Spain
- Email: luisd.lopez@icmat.es
- Received by editor(s): December 15, 2014
- Received by editor(s) in revised form: November 2, 2015
- Published electronically: March 17, 2016
- Additional Notes: This work was partially supported by the European Research Council ERC StG-256997-CZOSQP, the Spanish grant MTM2010-16518 and by ICMAT Severo Ochoa Grant SEV-2011-0087 (Spain)
- Communicated by: Marius Junge
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3869-3885
- MSC (2010): Primary 42B20, 42B25, 42C40, 46L51, 46L52
- DOI: https://doi.org/10.1090/proc/13073
- MathSciNet review: 3513545