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$L^p$ estimates for a class of oscillatory integrals


Author: G. Sampson
Journal: Proc. Amer. Math. Soc. 131 (2003), 2727-2732
MSC (2000): Primary 42B20; Secondary 46B70, 47G10
Published electronically: April 9, 2003
MathSciNet review: 1974329
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain a simpler proof of Theorem 3.1 of The complete $(L^p,L^p)$ mapping properties of some oscillatory integrals in several dimensions, by G. Sampson and P. Szeptycki (Canad. Math. J. 53 (5) (2001), 1031-1056).


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  • [SS] G. Sampson and P. Szeptycki, The complete (𝐿^{𝑝},𝐿^{𝑝}) mapping properties of some oscillatory integrals in several dimensions, Canad. J. Math. 53 (2001), no. 5, 1031–1056. MR 1859765, 10.4153/CJM-2001-040-9
  • [St] 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

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Additional Information

G. Sampson
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
Email: sampsgm@math.auburn.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07131-4
Keywords: Oscillatory integrals, $L^p$ mappings
Received by editor(s): December 26, 2001
Published electronically: April 9, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society