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Book Information

Author(s): Antoni Zygmund
Title: Trigonometric series, Vols. I, II
Additional book information: third edition, with a foreword by Robert Fefferman, Cambridge Mathematical Library, Cambridge University Press, 2002, (Vol. I) xiv + 383 pp., (Vol. II) viii + 364, $60.00, 0-521-89053-5

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4.: Fourier analysis and related topics, 2002, Banach Center Publications volume 56, Institute of Mathematics, Polish Academy of Sciences. MR 2003k:42002
5.: C.C. GRAHAM and O.C. Mc GEHEE. Essays in commutative harmonic analysis. 1979, Springer-Verlag. MR 81d:43001
6.: H. HELSON. Harmonic analysis. 1983, Addison-Wesley. MR 85e:43001
7.: E. HEWITT and K.A. ROSS. Abstract harmonic analysis, I, II. 1963, 1970, Springer-Verlag. MR 28:158, MR 41:7378
8.: J.-P. KAHANE. Séries de Fourier absolûment convergentes. 1970, Springer-Verlag. MR 43:801
9.: J.-P. KAHANE and R. SALEM. Ensembles parfaits et séries trigonométriques. 1963 and 1994, Hermann. MR 28:3279, MR 96e:42001
10.: Y. KATZNELSON. An introduction to harmonic analysis. 1968, Wiley, New edition 2004, Cambridge University Press. MR 40:1734
11.: J.M. LOPEZ and R.A. ROSS. Sidon sets. 1975, Marcel Dekker. MR 55:13173
12.: M.B. MARCUS and G. PISIER. Random Fourier series with applications to harmonic analysis. 1981, Princeton University Press. MR 83b:60031
13.: Y. MEYER. Algebraic numbers and harmonic analysis. 1972, North-Holland. MR 58:5579
14.: W. RUDIN. Fourier analysis on groups. 1962, Interscience Publishers. MR 27:2808
15.: E.M. STEIN. Harmonic analysis, real-variable methods, orthogonality and oscillatory integrals. 1993, Princeton University Press. MR 95c:42002
16.: E.M. STEIN and R. SHAKARCHI. Fourier analysis, an introduction. 2003, Princeton University Press. MR 2004a:42001
17.: N.Y. ANTONOV. Convergence of Fourier series. East Journal on Approximations 2 (1996), 187-196. MR 97h:42005
18.: M. ASH and G. WANG. A survey of uniqueness questions in multiple trigonometric series. in Contemporary Mathematics 208 (1997), American Mathematical Society, 35-71. MR 99f:42019
19.: M. ASH and G. WANG. Some spherical uniqueness theorems for multiple trigonometric series. Annals of Mathematics 151 (2000), 1-33. MR 2001a:42009
20.: S.V. BOCHKAREV. Everywhere divergent Fourier-Walsh series. Doklady Mathematics 67 n $^{\circ}$ 3 (2003), 307-310.
21.: J. BOURGAIN. Sidon sets and Riesz products. Ann. Inst. Fourier 35 (1) (1985) 136-148. MR 86h:43009
22.: L. CARLESON. Convergence and growth of partial sums of Fourier series. Acta Mathematica 116 (1966), 135-157. MR 33:7774
23.: S. JAFFARD and Y. MEYER. Wavelet methods for pointwise regularity and local oscillations of functions. Memoir Amer. Math. Soc. 587 (1996). MR 97d:42005
24.: S.V. KONYAGIN. On everywhere divergence of trigonometric Fourier series. Sbornik Math. 191 (2000), 97-120. MR 2001e:42007
25.: H. LEBESGUE. Sur les intégrales singulières. Annales de la Faculté des Sciences de Toulouse (3) 1 (1909), 25-117.
26.: R. SALEM. Review: Trigonometric series (A. Zygmund), Bulletin American Mathematical Society 66 (1960), 6-12.

Reviewer(s):
Jean-Pierre Kahane
Affiliation: Université Paris-Sud
Email: jean-pierre.kahane@math.u-psud.fr

MSC (2000): Primary 42A16, 42A20, 42A24, 42A32, 42A33, 42A38, 42A50, 42A55, 42A63, 42B05, 42B10, 42B25
DOI: 10.1090/S0273-0979-04-01013-4
PII: S 0273-0979(04)01013-4
Posted: March 4, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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