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Operators associated to flat plane curves: \(L^ p\) estimates via dilation methods. (English) Zbl 0723.44006

The authors give a new sufficient condition for the \(L^ p\)-boundedness of the Hilbert transform and for the maximal operator associated to a class of continuous plane curves. Also an example of a Hilbert transform that is continuous in \(L^ p\) only for \(p=2\) is given.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
42B25 Maximal functions, Littlewood-Paley theory
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