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Norm estimates and representations for Calderón-Zygmund operators using averages over starlike sets

Author(s): David K. Watson; Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 351 (1999), 4127-4171.
MSC (1991): Primary 42B20, 42B25
Posted: July 1, 1999
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Abstract: We show that homogeneous singular integrals may be represented in terms of averages over starlike sets. This permits us to use the geometry of starlike sets to derive operator-specific weighted norm inequalities.

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Additional Information:

David K. Watson
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
Email: watsondk@member.ams.org

Richard L. Wheeden
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
Email: wheeden@math.rutgers.edu

DOI: 10.1090/S0002-9947-99-02313-2
PII: S 0002-9947(99)02313-2
Received by editor(s): December 30, 1996 and, in revsied form, December 15, 1997
Posted: July 1, 1999
Additional Notes: Supported in part by NSF Grant DMS95--00799
Copyright of article: Copyright 1999, American Mathematical Society

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