Sobolev estimates for operators given by averages over cones
HTML articles powered by AMS MathViewer
- by Scipio Cuccagna PDF
- Trans. Amer. Math. Soc. 350 (1998), 935-946 Request permission
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
- Victor Guillemin, Cosmology in $(2 + 1)$-dimensions, cyclic models, and deformations of $M_{2,1}$, Annals of Mathematics Studies, vol. 121, Princeton University Press, Princeton, NJ, 1989. MR 999388, DOI 10.1515/9781400882410
- Allan Greenleaf and Gunther Uhlmann, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J. Funct. Anal. 89 (1990), no. 1, 202–232. MR 1040963, DOI 10.1016/0022-1236(90)90011-9
- Allan Greenleaf and Gunther Uhlmann, Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms. II, Duke Math. J. 64 (1991), no. 3, 415–444. MR 1141280, DOI 10.1215/S0012-7094-91-06422-7
- D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta Math. 157 (1986), no. 1-2, 99–157. MR 857680, DOI 10.1007/BF02392592
- Christopher D. Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, vol. 105, Cambridge University Press, Cambridge, 1993. MR 1205579, DOI 10.1017/CBO9780511530029
- C. D. Sogge and E. M. Stein, Averages over hypersurfaces. Smoothness of generalized Radon transforms, J. Analyse Math. 54 (1990), 165–188. MR 1041180, DOI 10.1007/BF02796147
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
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
- Received by editor(s): September 30, 1994
- Received by editor(s) in revised form: April 4, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 935-946
- MSC (1991): Primary 42B20, 26A33; Secondary 53C65
- DOI: https://doi.org/10.1090/S0002-9947-98-01784-X
- MathSciNet review: 1390975