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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sobolev estimates for operators
given by averages over cones


Author: Scipio Cuccagna
Journal: Trans. Amer. Math. Soc. 350 (1998), 935-946
MSC (1991): Primary 42B20, 26A33; Secondary 53C65
MathSciNet review: 1390975
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Abstract: We prove a result related to work by A. Greenleaf and G. Uhlmann concerning Sobolev estimates for operators given by averages over cones. This is done using the almost orthogonality lemma of Cotlar and Stein, and the van der Corput lemma on oscillatory integrals.


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Additional Information

Scipio Cuccagna
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: cuccagna@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01784-X
PII: S 0002-9947(98)01784-X
Keywords: Distributions, pseudodifferential operator, oscillatory integral, stationary phase, interpolation theorems for operators, conormal bundle
Received by editor(s): September 30, 1994
Received by editor(s) in revised form: April 4, 1996
Article copyright: © Copyright 1998 American Mathematical Society