Book Review
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MathSciNet review:
1568090
Full text of review:
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Book Information:
Author:
Christopher Sogge
Title:
Fourier integrals in classical analysis
Additional book information:
Cambridge University Press, Cambridge, 1993, x+237 pp., US$39.95. ISBN 0-521-43464-5.
J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69–85. MR 874045, DOI 10.1007/BF02792533
Anthony Carbery, The boundedness of the maximal Bochner-Riesz operator on $L^{4}(\textbf {R}^{2})$, Duke Math. J. 50 (1983), no. 2, 409–416. MR 705033
J. J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences, New York University, New York, 1973. Translated from Dutch notes of a course given at Nijmegen University, February 1970 to December 1971. MR 0451313
Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36. MR 257819, DOI 10.1007/BF02394567
Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI 10.1007/BF02392052
Lars Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), no. 1, 21–64. MR 686819, DOI 10.1080/03605308308820262
David Jerison, Carleman inequalities for the Dirac and Laplace operators and unique continuation, Adv. in Math. 62 (1986), no. 2, 118–134. MR 865834, DOI 10.1016/0001-8708(86)90096-4
Akihiko Miyachi, On some estimates for the wave equation in $L^{p}$ and $H^{p}$, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), no. 2, 331–354. MR 586454
Gerd Mockenhaupt, Andreas Seeger, and Christopher D. Sogge, Wave front sets, local smoothing and Bourgain’s circular maximal theorem, Ann. of Math. (2) 136 (1992), no. 1, 207–218. MR 1173929, DOI 10.2307/2946549
Gerd Mockenhaupt, Andreas Seeger, and Christopher D. Sogge, Local smoothing of Fourier integral operators and Carleson-Sjölin estimates, J. Amer. Math. Soc. 6 (1993), no. 1, 65–130. MR 1168960, DOI 10.1090/S0894-0347-1993-1168960-6
Juan C. Peral, $L^{p}$ estimates for the wave equation, J. Functional Analysis 36 (1980), no. 1, 114–145. MR 568979, DOI 10.1016/0022-1236(80)90110-X
Christopher D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), no. 2, 349–376. MR 1098614, DOI 10.1007/BF01245080
Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
Robert S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), no. 3, 705–714. MR 512086
- [1]
- J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69-85. MR 874045 (88f:42036)
- [2]
- A. Carbery, The boundedness of the maximal Bochner-Riesz operator on
, Duke Math. J. 50 (1983), 409-416. MR 705033 (84m:42025)
- [3]
- J. J. Duistermaat, Fourier integral operators, New York Univ., New York, 1973. MR 0451313 (56:9600)
- [4]
- C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36. MR 0257819 (41:2468)
- [5]
- L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), 79-183.. MR 0388463 (52:9299)
- [6]
- -, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), 21-64. MR 686819 (85c:35018)
- [7]
- D. Jerison, Carlemann inequalities for the Dirac and Laplace operators and unique continuation, Adv. Math. 63 (1986), 118-134. MR 865834 (88b:35218)
- [8]
- A. Miyachi, On some estimates for the wave equation in
and
, J. Fac. Sci. Tokyo 27 (1980), 331-354. MR 586454 (83g:35060)
- [9]
- G. Mockenhaupt, A. Seeger, and C. Sogge, Wave front sets, local smoothing and Bourgain's circular maximal theorem, Ann. of Math. (2) 136 (1992), 207-218. MR 1173929 (93i:42009)
- [10]
- -, Local smoothing of Fourier integral operators and Carleson-Sjölin estimates, J. Amer. Math. Soc. 6 (1993), 65-130. MR 1168960 (93h:58150)
- [11]
- J. Peral,
estimates for the wave equation, J. Funct. Anal. 36 (1980,), 114-145. MR 568979 (81k:35089)
- [12]
- C. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 346-376. MR 1098614 (92i:58192)
- [13]
- E. Stein, Maximal functions: spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 2174-2175. MR 0420116 (54:8133a)
- [14]
- R. Strichartz, Restrictions of Fourier transforms to quadratic surfaces, Duke Math. J. 44 (1977), 705-714. MR 0512086 (58:23577)
Review Information:
Reviewer:
Allan Greenleaf
Journal:
Bull. Amer. Math. Soc.
30 (1994), 255-258
DOI:
https://doi.org/10.1090/S0273-0979-1994-00458-6