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Operator-valued dyadic harmonic analysis beyond doubling measures


Authors: José M. Conde-Alonso and Luis Daniel López-Sánchez
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
Published electronically: March 17, 2016
MathSciNet review: 3513545
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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.


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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
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

DOI: https://doi.org/10.1090/proc/13073
Keywords: Operator-valued, von Neumann algebras, noncommutative $L_p$ spaces, Schatten classes, generalized Haar systems, Haar shift operators, nondoubling measures, Calder\'on-Zygmund decomposition.
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
Article copyright: © Copyright 2016 American Mathematical Society