Weak $(1,1)$ estimate for oscillatory singular integrals with real-analytic phases
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- by Yibiao Pan PDF
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Abstract:
In this paper, we prove the uniform weak $(1,\;1)$ estimate for oscillatory singular integral operators with real-analytic phase functions in the one-dimensional case. Some partial results for the higher-dimensional case is also included.References
- Sagun Chanillo and Michael Christ, Weak $(1,1)$ bounds for oscillatory singular integrals, Duke Math. J. 55 (1987), no. 1, 141–155. MR 883667, DOI 10.1215/S0012-7094-87-05508-6
- Sagun Chanillo, Douglas S. Kurtz, and Gary Sampson, Weighted weak $(1,1)$ and weighted $L^p$ estimates for oscillating kernels, Trans. Amer. Math. Soc. 295 (1986), no. 1, 127–145. MR 831193, DOI 10.1090/S0002-9947-1986-0831193-7
- Michael Christ, Weak type $(1,1)$ bounds for rough operators, Ann. of Math. (2) 128 (1988), no. 1, 19–42. MR 951506, DOI 10.2307/1971461
- Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36. MR 257819, DOI 10.1007/BF02394567
- Robert M. Hardt, Slicing and intersection theory for chains associated with real analytic varieties, Acta Math. 129 (1972), 75–136. MR 315561, DOI 10.1007/BF02392214
- Alexander Nagel and Stephen Wainger, Hilbert transforms associated with plane curves, Trans. Amer. Math. Soc. 223 (1976), 235–252. MR 423010, DOI 10.1090/S0002-9947-1976-0423010-8
- Yibiao Pan, Uniform estimates for oscillatory integral operators, J. Funct. Anal. 100 (1991), no. 1, 207–220. MR 1124299, DOI 10.1016/0022-1236(91)90108-H
- 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
- Fulvio Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), no. 1, 179–194. MR 890662, DOI 10.1016/0022-1236(87)90064-4
- E. M. Stein, Oscillatory integrals in Fourier analysis, Beijing lectures in harmonic analysis (Beijing, 1984) Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 307–355. MR 864375
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 789-802
- MSC: Primary 42B20; Secondary 47G10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169044-6
- MathSciNet review: 1169044