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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hilbert transforms and maximal functions along variable flat curves


Author: Jonathan M. Bennett
Journal: Trans. Amer. Math. Soc. 354 (2002), 4871-4892
MSC (2000): Primary 44A12, 42B20
Published electronically: July 16, 2002
MathSciNet review: 1926840
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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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Additional Information

Jonathan M. Bennett
Affiliation: Department of Mathematics and Statistics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland

DOI: https://doi.org/10.1090/S0002-9947-02-03087-8
Received by editor(s): May 4, 1999
Published electronically: July 16, 2002
Additional Notes: Partially supported by EPSRC Grant GR/L10024
Article copyright: © Copyright 2002 American Mathematical Society