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 | References | Similar Articles | Additional Information

Abstract: We study certain Hilbert transforms and maximal functions along variable flat curves in the plane. We obtain their 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:
http://dx.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