-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves

Author:
Neal Bez

Journal:
Proc. Amer. Math. Soc. **135** (2007), 151-161

MSC (2000):
Primary 42B15

DOI:
https://doi.org/10.1090/S0002-9939-06-08603-5

Published electronically:
June 20, 2006

MathSciNet review:
2280201

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Some sufficient conditions on a real polynomial and a convex function are given in order for the Hilbert transform and maximal operator along to be bounded on , for all in , with bounds independent of the coefficients of . The same conclusion is shown to hold for the corresponding hypersurface in under weaker hypotheses on .

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Additional Information

**Neal Bez**

Affiliation:
School of Mathematics, University of Edinburgh, Kings’s Buildings, Edinburgh, EH3 9JZ United Kingdom

Email:
n.r.bez@sms.ed.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-06-08603-5

Received by editor(s):
July 26, 2005

Published electronically:
June 20, 2006

Additional Notes:
The author was supported by an EPSRC award

Communicated by:
Michael Lacey

Article copyright:
© Copyright 2006
American Mathematical Society