Book Review
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Book Information:
Author:
E. Stein
Title:
Harmonic analysis real-variable methods, orthogonality, and oscillatory integrals
Additional book information:
Princeton Univ. Press,
Princeton, NJ,
1993,
xiii+695 pp.,
ISBN 0-691-03216-5,
$85.00$
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
Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 141789, DOI 10.2307/1970375
Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157. MR 199631, DOI 10.1007/BF02392815
Ronald R. Coifman, A real variable characterization of $H^{p}$, Studia Math. 51 (1974), 269–274. MR 358318, DOI 10.4064/sm-51-3-269-274
R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5
Guy David and Jean-Lin Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371–397. MR 763911, DOI 10.2307/2006946
E. B. Fabes and N. M. Rivière, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19–38. MR 209787, DOI 10.4064/sm-27-1-19-38
Charles Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587–588. MR 280994, DOI 10.1090/S0002-9904-1971-12763-5
Charles Fefferman, The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330–336. MR 296602, DOI 10.2307/1970864
C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
Richard A. Hunt, On the convergence of Fourier series, Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967) Southern Illinois Univ. Press, Carbondale, Ill., 1968, pp. 235–255. MR 0238019
Richard Hunt, Benjamin Muckenhoupt, and Richard Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227–251. MR 312139, DOI 10.1090/S0002-9947-1973-0312139-8
F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
D. H. Phong and E. M. Stein, The Newton polyhedron and oscillatory integral operators, Acta Math. 179 (1997), no. 1, 105–152. MR 1484770, DOI 10.1007/BF02392721
Helmut Schulz, Convex hypersurfaces of finite type and the asymptotics of their Fourier transforms, Indiana Univ. Math. J. 40 (1991), no. 4, 1267–1275. MR 1142714, DOI 10.1512/iumj.1991.40.40056
Andreas Seeger, Christopher D. Sogge, and Elias M. Stein, Regularity properties of Fourier integral operators, Ann. of Math. (2) 134 (1991), no. 2, 231–251. MR 1127475, DOI 10.2307/2944346
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
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163–196. MR 223492, DOI 10.2307/2373431
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
A. N. Varčenko, Newton polyhedra and estimates of oscillatory integrals, Funkcional. Anal. i Priložen. 10 (1976), no. 3, 13–38 (Russian). MR 0422257
- [B]
- J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Anal. Math. 47 (1986), 69-85. MR 88f:42036
- [Ca1]
- L. Carleson, Interpolation by bounded analytic functions and the corona problem, Ann. of Math. 76 (1962), 547-559. MR 25:5186
- [Ca2]
- L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157. MR 0199631
- [Co]
- R.R. Coifman, A real-variable characterization of
, Studia Math. 51 (1974), 269-274. MR 50:10784
- [CF]
- R.R. Coifman, C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 50:10670
- [CW]
- R.R. Coifman, G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 56:6264
- [DJ]
- G. David, J.-L. Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. 120 (1984), 371-397. MR 85k:42041
- [FR]
- E. Fabes, N. Rivière, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19-38. MR 35:683
- [F1]
- C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587-588. MR 43:6713
- [F2]
- C. Fefferman, The multiplier problem for the ball, Ann. of Math. 94 (1971), 330-336. MR 45:5661
- [FS]
- C. Fefferman, E.M. Stein,
spaces of several variables, Acta Math. 129 (1972), 137-193. MR 56:6263
- [Ho]
- L. Hörmander, Hypoelliptic second-order differential equations, Acta Math. 119 (1967), 147-171. MR 36:5526
- [Hu]
- R. Hunt, On the convergence of Fourier series, in ``Orthogonal Expansions and Their Continuous Analogues'' (D. Haimo ed.) Southern Illinois Univ. Press, Carbondale, IL (1968), 235-255. MR 38:6296
- [HMW]
- R. Hunt, B. Muckenhoupt, R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251. MR 47:701
- [JN]
- F. John, L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. MR 24:A1348
- [KS]
- A.W. Knapp, E.M. Stein, Intertwining operators for semi-simple groups, Ann. of Math. 93 (1971), 489-578. MR 57:536
- [L]
- H. Lewy, An example of a smooth linear partial differential equation without solutions, Ann. of Math. 66 (1957), 155-158. MR 19:551d
- [M]
- B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. MR 45:2461
- [PS]
- D.H. Phong, E.M. Stein, The Newton polyhedron and oscillatory integral operators, Acta Math. 179 (1997), 105-152. MR 98j:42009
- [Sc]
- H. Schulz, Convex hypersurfaces of finite type and the asymptotics of their Fourier transforms, Indiana Univ. Math. J. 40 (1991), 1267-1275. MR 93a:42007
- [SSS]
- A. Seeger, C. Sogge, E.M. Stein, Regularity properties of Fourier integral operators, Ann. of Math. 134 (1991), 231-251. MR 92g:35252
- [S1]
- E.M. Stein, Maximal functions: Spherical means, Proc. Natl. Acad. Sci. U.S.A. 73 (1976), 2174-2175. MR 54:8133a
- [S2]
- E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970. MR 0290095
- [SW1]
- E.M. Stein, G. Weiss, Generalizations of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163-196. MR 36:6540
- [SW2]
- E.M. Stein, G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971. MR 46:4102
- [V]
- A.N. Varcenko, Newton polyhedra and estimation of oscillatory integrals, Funct. Anal. Appl. 10 (1976), 175-196. MR 54:10248
Review Information:
Reviewer:
Fulvio Ricci
Affiliation:
Politecnico di Torino
Email:
fricci@polito.it
Journal:
Bull. Amer. Math. Soc.
36 (1999), 505-521
DOI:
https://doi.org/10.1090/S0273-0979-99-00792-2
Published electronically:
July 21, 1999
Review copyright:
© Copyright 1999
American Mathematical Society