Hilbert transforms and maximal functions along variable flat curves

Bennett, Jonathan

doi:10.1090/S0002-9947-02-03087-8

Hilbert transforms and maximal functions along variable flat curves
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Trans. Amer. Math. Soc. 354 (2002), 4871-4892 Request permission

Abstract:

We study certain Hilbert transforms and maximal functions along variable flat curves in the plane. We obtain their $L^{2}(\mathbb {R}^{2})$ boundedness by considering the oscillatory singular integrals which arise from an application of a partial Fourier transform.

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