Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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

References [Enhancements On Off] (What's this?)

  • [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 33:7774
  • [Co] R.R. Coifman, A real-variable characterization of $H^{p}$, 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, $H^{p}$ 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 44:7280
  • [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
MSC (1991): Primary 42B20, 42B25, 35S05, 35S30
DOI: https://doi.org/10.1090/S0273-0979-99-00792-2
Published electronically: July 21, 1999
Review copyright: © Copyright 1999 American Mathematical Society
American Mathematical Society