$L^ p$-boundedness of the Hilbert transform and maximal function associated to flat plane curves
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- by S. Ziesler PDF
- Proc. Amer. Math. Soc. 122 (1994), 1035-1043 Request permission
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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Additional 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