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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ L\sp p$-boundedness of the Hilbert transform and maximal function associated to flat plane curves


Author: S. Ziesler
Journal: Proc. Amer. Math. Soc. 122 (1994), 1035-1043
MSC: Primary 42B10; Secondary 47G10
DOI: https://doi.org/10.1090/S0002-9939-1994-1213872-5
MathSciNet review: 1213872
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Abstract: We give a sufficient condition for the Hilbert transform and maximal function associated to a flat plane convex curve $ \Gamma (t) = (t,\gamma (t))$ to be bounded on $ {L^p},1 < p < \infty $. Our result includes the previously known sufficient conditions, i.e., $ \gamma'$ doubling or h, defined by $ h(t) = t\gamma'(t) - \gamma (t),t > 0$, infinitesimally doubling, as special cases.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1213872-5
Article copyright: © Copyright 1994 American Mathematical Society