Vector 𝐴₂ weights and a Hardy-Littlewood maximal function

Christ, Michael; Goldberg, Michael

doi:10.1090/S0002-9947-01-02759-3

Vector $A_2$ weights and a Hardy-Littlewood maximal function
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by Michael Christ and Michael Goldberg

Trans. Amer. Math. Soc. 353 (2001), 1995-2002

DOI: https://doi.org/10.1090/S0002-9947-01-02759-3

Published electronically: January 5, 2001

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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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