Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$L^ p$-boundedness of the Hilbert transform and maximal function associated to flat plane curves
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by S. Ziesler
Proc. Amer. Math. Soc. 122 (1994), 1035-1043
DOI: https://doi.org/10.1090/S0002-9939-1994-1213872-5

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.
References
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Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • 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