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On Fourier multiplier transformations of Banach-valued functions


Author: Terry R. McConnell
Journal: Trans. Amer. Math. Soc. 285 (1984), 739-757
MSC: Primary 42B15; Secondary 46E40
DOI: https://doi.org/10.1090/S0002-9947-1984-0752501-X
MathSciNet review: 752501
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Abstract: We obtain analogues of the Mihlin multiplier theorem and Littlewood-Paley inequalities for functions with values in a suitable Banach space $ B$. The requirement on $ B$ is that it have the unconditionality property for martingale difference sequences.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0752501-X
Keywords: Fourier multiplier, martingale transform, $ {L^p}$ inequalities, vector-valued function, unconditionality
Article copyright: © Copyright 1984 American Mathematical Society

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