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Hilbert transforms and maximal functions along variable flat curves

Authors:	Jonathan M Bennett

Institution:	Department of Mathematics and Statistics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland

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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