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Sobolev estimates for operators given by averages over cones
Author(s):
Scipio
Cuccagna
Journal:
Trans. Amer. Math. Soc.
350
(1998),
935-946.
MSC (1991):
Primary 42B20, 26A33;
Secondary 53C65
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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.
References:
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- A.Greenleaf and G.Uhlmann, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J.Funct.Anal. 89 (1990), 202-232. MR 91i:58146
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- A.Greenleaf and G.Uhlmann, Composition of some singular Fourier integral operators and estimates for restricted x-ray transforms, II, Duke Math.Jour. 64 (1991), 415-444. MR 93b:58146
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- D.H.Phong and E.M.Stein, Hilbert integrals, singular integrals, and Radon transforms I, Acta Math. 157 (1986), 99-157. MR 88i:42028a
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- C.D.Sogge, Fourier Integrals in Classical Analysis, Cambridge Univ. Press, 1993. MR 94c:35178
- [SS]
- C.D.Sogge and E.M.Stein, Averages over hypersurfaces: Smoothness of generalized Radon transforms, J. Analyse Math. 54 (1990), 165-188. MR 91i:58145
- [St]
- E.M.Stein, Harmonic Analysis: real variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, 1993. MR 95c:42002
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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