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Vector $A_2$ weights and a Hardy-Littlewood maximal function


Authors: Michael Christ and Michael Goldberg
Journal: Trans. Amer. Math. Soc. 353 (2001), 1995-2002
MSC (2000): Primary 42B25
DOI: https://doi.org/10.1090/S0002-9947-01-02759-3
Published electronically: January 5, 2001
MathSciNet review: 1813604
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Abstract:

An analogue of the Hardy-Littlewood maximal function is introduced, for functions taking values in finite-dimensional Hilbert spaces. It is shown to be $L^2$ bounded with respect to weights in the class $A_2$ of Treil, thereby extending a theorem of Muckenhoupt from the scalar to the vector case.


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Additional Information

Michael Christ
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: mchrist@math.berkeley.edu

Michael Goldberg
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: mikeg@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02759-3
Received by editor(s): June 22, 2000
Published electronically: January 5, 2001
Additional Notes: The first author was supported in part by NSF grant DMS-9970660. He thanks the staff of the Bamboo Garden hotel in Shenzhen, PRC, for the hospitable atmosphere in which a portion of this work was done
The second author was supported by an NSF graduate fellowship
Article copyright: © Copyright 2001 American Mathematical Society

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