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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example of a Hilbert transform


Author: Krzysztof Samotij
Journal: Proc. Amer. Math. Soc. 112 (1991), 965-972
MSC: Primary 42A50; Secondary 44A15
MathSciNet review: 1065092
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Abstract: We construct a nonnegative integrable function on the real line $ \mathbf{R}$ whose Hilbert transform cannot be almost everywhere dominated by the HardyLittlewood maximal function of any finite measure on $ \mathbf{R}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1065092-2
PII: S 0002-9939(1991)1065092-2
Article copyright: © Copyright 1991 American Mathematical Society